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The phase transitions are studied for the D-brane systems with multipleopen-string moduli in terms of toric geometry: between the parallel D-branephase corresponding to the Coulomb branch and the coincident phasecorresponding to the Higgs branch. The two separated D-branes on compactCalabi-Yau 3-fold coincide developing the geometric singularity in thecorresponding F-theory Calabi-Yau 4-fold in terms of TypeII/F theory duality,and the enhancement of gauge group $U(1)\times U(1)\rightarrow SU(2)$ in termsof gauge theory. For several D-brane system with various closed-string moduli,using the mirror symmetry and the typeII/F theory duality the A-modelsuperpotentials are obtained from the B-model side for the two phases, and theOoguri-Vafa invariants are extracted from the A-model superpotential. We findthe discrete $Z_2$ symmetry of superpotentials in the two parallel D-branesphase of all the models which is a signal of decoupling of the paralleltopological D-branes. Furthermore, the \emph{$U(1)$ Ooguri-Vafa invariants} forone of the two parallel D-branes are the same as the invariants for the D-branesystem with only one D-brane. However they are different from the \emph{$SU(2)$Ooguri-Vafa invariants} corresponding to the two D-branes coincident phase. Wepresent these Ooguri-Vafa invariants for two phases with figures to observe thedifference, and find that in two phases the points for invariants form awave-packet respectively. The wave-packets for coincident phase are higher andwider than ones for parallel phase which means more complicate spectrumstructure. This is an evidence of the phase transition between the Coulombbranch and the Higgs branch.

D-brane superpotentials, SU(2) Ooguri-Vafa invariants and TypeII/F -theory duality