After Bespin will Anakin get his old lightsaber back or will he continue to use his current one?
That’s Luke’s lightsaber now, and Luke is going to keep it. Anakin wants him to, but there’s also the fact that, for a while after Bespin, Anakin will still be undercover, so of course he’ll have to stick with his Sith lightsaber.
After the fall of the Empire, though…he could just replace the crystal in his Sith lightsaber, I suppose, but I honestly think he’ll want to get rid of it, so he’ll probably build a new one from scratch. (So then all three Skywalkers will have an Anakin Skywalker original, since Anakin builds Leia a lightsaber using Obi-Wan’s crystal post-ANH.)