Is the Ray-Singer analytic torsion for an arbitrary compact 3-manifold with finite Abelian fundamental group equivalent to the Ray-Singer analytic torsion of S^3 mod some direct product of Z_N's? It seems like Thurston's elliptization conjecture implies the answer is yes, but my understanding in this area is very limited. I am a physicist so please forgive me if I am being imprecise with terminology. References would also be very helpful.