
I also added some artwork of Mary holding her red "Easter" eggs, as well as some pictures of what is believed to be Lazarus' tomb, which can be viewed and toured even today.
The most conservative and safest interpretation is that there are two Marys and one unidentified "sinful woman." The next scenario, also very conservative and safe is that there are two Marys and that Mary of Bethany is also the "sinful woman." The next scenario, somewhat conservative but starting to read in between the lines is that there are still two Marys, with the "sinful woman" being Mary Magdalene. The fourth scenario, admittedly more of a stretch but still a real possibility is that the three entities are actually all one in the same- the idea that Mary of Bethany, Mary Magdalene, and the sinful woman are all the same person. This is what I personally hold to, though I believe that the other three are just as acceptable, don't change the point of the gospel whatsoever, and in at least the first two cases, are far more palatable and accepted. But I'd like to take some time to at least share with you my findings and why I think they are one.
In Luke 7 it simply calls the woman a "sinful woman." No name. However, in John 11.2, it says "This Mary, whose brother Lazarus now lay sick, was the same one who poured perfume on the Lord and wiped his feet with her hair." I believe that this instance wasn't speaking about the very similar instance in John 12 (which does in fact name her as a Mary) for four main reasons.
First, this text seems to be in chronological order, putting the raising of Lazarus before the second instance of anointing Jesus' feet. The text in John 11 says "poured" past tense rather than "will pour" as an event in the future.
Secondly, it makes mention that Lazarus was there, who had been raise from the dead. It speaks of it being an event in the past.
Thirdly, why I don't think this statement of her being "the same one who poured perfume on Him" is mentioning a future event is because it seems to me that if he was to mention her as the one who would eventually anoint Him, he would make a note that it was a future event, like he did when he mentioned a future event in chapter 12 that Judas would be a part of when he said “one of His disciples, Judas Iscariot, who would betray Him.” In the case of Mary, it seems that he would have said something like “this Mary, whose brother now lay sick, is the same one who would pour perfume on Him,” rather than speak as if it were a past even. It would be similar to him saying “Judas Iscariot, who betrayed Him” even though it hadn’t happened. That wasn’t John’s writing style, per se.
Lastly, I think it would be an unnecessary point for John to point out that this is the same Mary as in the chapter 12 anointing because it is quite obvious that it’s the same Mary. No reason to make special mention. Due to the almost certainty that the gospel of John is the oldest, he may be making mention of this to tie up a loose end from Luke’s writing, reminding people that this Mary was the same one from Luke’s writing, since Luke didn't name her. Therefore, I don’t see it as differentiating Mary of Bethany from Mary Magdelene, but rather tying together Mary of Bethany with the “sinful woman.”
There are a couple reasons Luke may not have named the "sinful woman" by name. It is fairly common in the scriptures to name someone something else before certain experiences. Matthew was "the tax collector named Levi," Saul became Paul, Simon the Pharisee was first just mentioned as "the Pharisee" until Jesus speaks his name (which is so interesting to me, the text is technical until Jesus speaks and makes it personal, approaching a judgmental Pharisee as if to say, "I know your name, I know your life, I know who you are." Very cool). It is possible that before she encountered Christ and started following Him, Mary of Bethany was simply referred to as "the sinful woman."
It is also somewhat possible that the reason Luke didn't mention her name is because he wasn't there. He may have had his facts straight on many events that he was not present for, but decided to keep her anonymous. It could also be that she was maybe still alive and didn't want to defame her name, not that any of us have anything to hide, but you never know. John, who was probably there at the scene, may be clarifying this earlier writing of Luke by saying, "by the way, it was Mary of Bethany that was there anointing Jesus' feet."
Between these four observations, this makes it seem to me like this Mary, who poured perfume on the Lord was the same "sinful woman" mentioned in Luke 7.

First, both have a sister named Martha. I'm sure they probably weren't the only Mary and Martha sister duo, but the chances that it's a different Mary/Martha I wouldn't personally think would be very good.
Secondly, Martha in both texts is specifically described as "serving," making it seem like this Martha, mentioned in John 12, is the same Martha in the Mary and Martha story.
Thirdly, Mary's character is described similarly. Not that she's the only Mary in the world, or in the word for that matter, that had a very intimate devotion to Christ, but it builds the strength that this is almost definitely the same worshipful, devoted Mary who had a servant-hearted sister named Martha, both of whom enjoyed opening up their home to Jesus.
So far, it seems that the Mary in the Mary/Martha/Lazarus story is the same as the Mary/Martha story and the same as the "sinful woman."

Here is a writing from the Catholic Encyclopedia (CE) of 1910 that makes its case for the three Mary's being the same. I am unsure why they reversed their decision in 1969:
"Most of the Latins hold that these three were one and the same. Protestant critics, however, believe there were two, if not three, distinct persons. It is impossible to demonstrate the identity of the three; but those commentators undoubtedly go too far who assert, as does Westcott (on John 11:1), "that the identity of Mary with Mary Magdalene is a mere conjecture supported by no direct evidence, and opposed to the general tenor of the gospels [this excerpt from the CE is saying that the statement that Westcott has made that it is impossible to even think that these are the the same Mary is a very extreme and poor assessment on his part, as he even goes so far to say that it goes against the general purpose or concept of the gospels - Jobey]." It is the identification of Mary of Bethany with the "sinner" of Luke 7:37, which is most combatted by Protestants [which is interesting to me, because it seems very obvious that this is the "easy" one to deduce - Jobey].......
The first fact, mentioned in the Gospel relating to the question under discussion is the anointing of Christ's feet by a woman, a "sinner" in the city (Luke 7:37-50). This belongs to the Galilean ministry, it precedes the miracle of the feeding of the five thousand and the third Passover. Immediately afterwards St. Luke describes a missionary circuit in Galilee and tells us of the women who ministered to Christ, among them being "Mary who is called Magdalen, out of whom seven devils gone forth" (Luke 8:2); but he does not tell us that she is to be identified with the "sinner" of the previous chapter. In 10:38-42, he tells us of Christ's visit to Martha and Mary "in a certain town"; it is impossible to identify this town, but it is clear from 9:53, that Christ had definitively left Galilee, and it is quite possible that this "town" was Bethany. This seems confirmed by the preceding parable of the good Samaritan, which must almost certainly have been spoken on the road between Jericho and Jerusalem. But here again we note that there is no suggestion of an identification of the three persons (the "sinner", Mary Magdalene, and Mary of Bethany), and if we had only St. Luke to guide us we should certainly have no grounds for so identifying them. St. John, however, clearly identifies Mary of Bethany with the woman who anointed Christ's feet (12; cf. Matthew 26 and Mark 14).
It is remarkable that already in 11:2, St. John has spoken of Mary as "she that anointed the Lord's feet", [which in the Greek is] "he aleipsasa;" It is commonly said that he refers to the subsequent anointing which he himself describes in 12:3-8; but it may be questioned whether he would have used "he aleipsasa" if another woman, and she a "sinner" in the city, had done the same. It is conceivable that St. John, just because he is writing so long after the event and at a time when Mary was dead, wishes to point out to us that she was really the same as the "sinner." In the same way St. Luke may have veiled her identity precisely because he did not wish to defame one who was yet living; he certainly does something similar in the case of St. Matthew whose identity with Levi the publican (5:7) he conceals.
If the foregoing argument holds good, Mary of Bethany and the "sinner" are one and the same. But an examination of St. John's Gospel makes it almost impossible to deny the identity of Mary of Bethany with Mary Magdalen. From St. John we learn the name of the "woman" who anointed Christ's feet previous to the last supper. We may remark here that it seems unnecessary to hold that because St. Matthew and St. Mark say "two days before the Passover", while St. John says "six days" there were, therefore, two distinct anointings following one another. St. John does not necessarily mean that the supper and the anointing took place six days before, but only that Christ arrived at Bethany six days before the Passover. At that supper, then, Mary received the glorious encomium, "she hath wrought a good work upon Me . . . in pouring this ointment upon My body she hath done it for My burial . . . wheresoever this Gospel shall be preached . . . that also which she hath done shall be told for a memory of her.
Is it credible, in view of all this, that this Mary should have no place at the foot of the cross, nor at the tomb of Christ? Yet it is Mary Magdalene who, according to all the Evangelists, stood at the foot of the cross and assisted at the entombment and was the first recorded witness of the Resurrection. And while St. John calls her "Mary Magdalene" in 19:25, 20:1, and 20:18, he calls her simply "Mary" in 20:11 and 20:16. [A possible conclusion is drawn by the CE that Christ's statement of the honor she would receive by storing the perfume for His burial would translate into her being the one that was at the cross, took part in His burial, and witnessed the empty tomb. It is also noted that just because she isn't named as "Mary Magdalene" doesn't rule out that it is possibly her, due to the fact that sometimes John called her Mary Magdalene, sometimes he simply called her Mary - Jobey]."

Very interesting indeed, and definitely a topic up for differences. Definitely not an essential core belief that changes the way you view God or your faith. Definitely impossible to say they are for sure all three the same person, definitely impossible to say they are for sure two people, and definitely impossible to say they are for sure three people.
At the end of the day, when it comes to God and His word, I think that sometimes the point isn't finding out the answer, but the point, rather, is simply just looking for it. I know that God loves to be searched and chased. We won't ever be able to search the Unsearchable, but that should never stop us from trying anyways.
I hope that sheds a little light in case you were curious. :o) Good luck in your studies, send anything my way if you find anything interesting.
Slainte!