Good points, Bingo and rpvee. I especially agree with Bingo's point: there is no legacy to Anakin's saber at all. It would have been great to have seen Anakin construct it, and carry it with him throughout the saga, and as rpvee put it so nicely, change the fate of the galaxy.
Maybe it would be an idea for an AOTC edit to show Anakin with a green lightsaber, and have him have a blue one in ROTS, so we can assume he built a new one? The one he has in ROTS now is just the spare he got on Geonosis.
I like Bob's idea to give Anakin a red saber, but I also agree that it's not really needed for the story. Sure it would look cool, but only if it can be made to work. As cool as Bob's work is, I don't really see it work.
Also funny how everybody is saying that it's ok to just assume Obi-Wan just retrieved Anakin's saber at some point between ROTS and ANH, while everybody was all over Lucas when he forgot to film Obi-Wan picking up the saber. And when would Obi-Wan get the saber? If we'd go Bob's route, the saber would be on Coruscant, and Obi-Wan was stuck on Tatooine at the end of ROTS.