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Abstract. We give a mathematically rigorous proof of Nekrasov's conjecture: the integration in the equivariant cohomology over the moduli spaces of instantons on R 4 gives a deformation of the Seiberg-Witten prepotential for N = 2 SUSY Yang-Mills theory. Through a study of moduli spaces on the blowup of R 4 , we derive a differential equation for the Nekrasov's partition function. It is a deformation of the equation for the Seiberg-Witten prepotential, found by Losev et al., and further studied by Gorsky et al.

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