  We calculate the topological string amplitudes of Calabi-Yau toric threefolds
corresponding to 4D, N=2, SU(2) gauge theory with N_f=0,1,2,3,4 fundamental
hypermultiplets by using the method of the geometric transition and show that
they reproduce Nekrasov's formulas for instanton counting. We also determine
the asymptotic forms of the Gopakumar-Vafa invariants of the Calabi-Yau
threefolds including those at higher genera from instanton amplitudes of the
gauge theory.
