  We continue the study of a class of geometric transitions proposed by
Aganagic and Vafa which exhibit open string instanton corrections to
Chern-Simons theory. In this paper we consider an extremal transition for a
local del Pezzo model which predicts a highly nontrivial relation between
topological open and closed string amplitudes. We show that the open string
amplitudes can be computed exactly using a combination of enumerative
techniques and Chern-Simons theory proposed by Witten some time ago. This
yields a striking conjecture relating the topological amplitudes of all genus
of the local del Pezzo model to a system of coupled Chern-Simons theories.
