Women Anointing Jesus: The Same Story?

The Gospels offer several stories of women who come to anoint Jesus. Some of these are clearly parallels, but one seems not to be.

The parallel stories are found in Matt. 26, Mark 14, Luke 7, and John 12. It is my argument that we have only two incidents reported, but by only two different women -- Mary the sister of Martha (Matthew, Mark and John), and an unnamed woman who was a sinner (Luke).

Some preliminary critical questions:

In conclusion: We have only two anointings and two women here, and while we have some differing focal points, we have no contradictions as such. The variations we see are no less or more than we would expect from stories that went through the process of oral tradition. (Though there are also signs, especially here, that John at least knew Mark's account; see here.)