  The phase transitions are studied for the D-brane systems with multiple
open-string moduli in terms of toric geometry: between the parallel D-brane
phase corresponding to the Coulomb branch and the coincident phase
corresponding to the Higgs branch. The two separated D-branes on compact
Calabi-Yau 3-fold coincide developing the geometric singularity in the
corresponding 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 terms
of gauge theory. For several D-brane system with various closed-string moduli,
using the mirror symmetry and the typeII/F theory duality the A-model
superpotentials are obtained from the B-model side for the two phases, and the
Ooguri-Vafa invariants are extracted from the A-model superpotential. We find
the discrete $Z_2$ symmetry of superpotentials in the two parallel D-branes
phase of all the models which is a signal of decoupling of the parallel
topological D-branes. Furthermore, the \emph{$U(1)$ Ooguri-Vafa invariants} for
one of the two parallel D-branes are the same as the invariants for the D-brane
system 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. We
present these Ooguri-Vafa invariants for two phases with figures to observe the
difference, and find that in two phases the points for invariants form a
wave-packet respectively. The wave-packets for coincident phase are higher and
wider than ones for parallel phase which means more complicate spectrum
structure. This is an evidence of the phase transition between the Coulomb
branch and the Higgs branch.
