  We give a mathematically rigorous proof of Nekrasov's conjecture: the
integration in the equivariant cohomology over the moduli spaces of instantons
on $\mathbb R^4$ 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
$\mathbb R^4$, 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.
