  It has been conjectured recently that the field theory limit of the
topological string partition functions, including all higher genus
contributions, for the family of CY3-folds giving rise to N=2 4D SU(N) gauge
theory via geometric engineering can be obtained from gauge instanton calculus.
We verify this surprising conjecture by calculating the partition functions for
such local CYs using diagrammatic techniques inspired by geometric transitions.
Determining the Gopakumar-Vafa invariants for these geometries to all orders in
the fiber wrappings allows us to take the field theory limit.
