  In this paper we demonstrate that the Stokes constants of unrefined free
energies and the Stokes constants of Nekrasov-Shatashvili free energies of
topological string on a non-compact Calabi-Yau threefold are identical,
possibly up to a sign, for any Borel singularity which is not associated to a
compact two-cycle that intersects only with non-compact four-cycles. Since the
Stokes constants of Nekrasov-Shatashvili free energies are conjectured to
coincide with those of quantum periods and therefore have the interpretation of
BPS invariants, our results give strong support that the Stokes constants of
unrefined free energies may also be identified with BPS invariants.
