If that happens then how Obi-wan gets the blue lightsaber is that Vader uses the sith lightsaber through the rest of the film and then at the very end of the duel just after obiwan says "it's over Anakin I have the high ground" when it takes a view from behind obiwan and you see Anakin from a distance just before it goes to him saying "you underestimate my power" have Anakin pull out and ignite the second lightsaber, because at that point he's so angry at Obiwan he'll do anything to show off his true power and kill obiwan, then he jumps at obiwan, gets legs cut, jedi lightsaber lands on the ground (as well as the sith lightsaber) and obiwan picks it up and at this point he's too distracted by the fact his apprentice has been all cut up, is shouting I hate you at him and is then burning to notice the Sith lightsaber, and then you assume that Sidious picks the Sith lightsaber up after the scene where he puts his hand on Anakin's head.
If that happens then how Obi-wan gets the blue lightsaber is that Vader uses the sith lightsaber through the rest of the film and then at the very end of the duel just after obiwan says "it's over Anakin I have the high ground" when it takes a view from behind obiwan and you see Anakin from a distance just before it goes to him saying "you underestimate my power" have Anakin pull out and ignite the second lightsaber, because at that point he's so angry at Obiwan he'll do anything to show off his true power and kill obiwan, then he jumps at obiwan, gets legs cut, jedi lightsaber lands on the ground (as well as the sith lightsaber) and obiwan picks it up and at this point he's too distracted by the fact his apprentice has been all cut up, is shouting I hate you at him and is then burning to notice the Sith lightsaber, and then you assume that Sidious picks the Sith lightsaber up after the scene where he puts his hand on Anakin's head.