  We obtain analytic and numerical results for the non-perturbative amplitudes
of topological string theory on arbitrary, compact Calabi-Yau manifolds. Our
approach is based on the theory of resurgence and extends previous special
results to the more general case. In particular, we obtain explicit
trans-series solutions of the holomorphic anomaly equations. Our results
predict the all orders, large genus asymptotics of the topological string free
energies, which we test in detail against high genus perturbative series
obtained recently in the compact case. We also provide additional evidence that
the Stokes constants appearing in the resurgent structure are closely related
to integer BPS invariants.
