"Hello everyone, I own a c650gt 2012, I would like to change the original manifold for a better sound, but are the manifolds compatible with the c600 for equivalent year?"
I think the Sport has a different rear exit angle than the GT. On the early ones like yours, it has a VERY LARGE collector under the bike and may not be easy to work with. I'm going to on my '20, remove the header and remove the CAT from the pipe. I will cut the pipe in front of the CAT and air chisel out the honeycomb material.
I've seen videos of the GT running without a muffler and it's really not much louder than with the muffler. I believe the CAT is very restrictive and db limiting.
Good luck with your project, Dan