Partition functions of N=1 gauge theories on S2 x Rε2 and duality

We compute the partition functions of N = 1 gauge theories on S-2 x R-epsilon(2) using supersymmetric localization. The path integral reduces to a sum over vortices at the poles of S-2 and at the origin of R-epsilon(2). The exact partition functions allow us to test Seiberg duality beyond the supersymmetric index. We propose the N = 1 partition functions on the Omega-background, and show that the Nekrasov partition functions can be recovered from these building blocks.