  We study the topological string on local P2 with O-plane and D-brane at its
real locus, using three complementary techniques. In the A-model, we refine
localization on the moduli space of maps with respect to the torus action
preserved by the anti-holomorphic involution. This leads to a computation of
open and unoriented Gromov-Witten invariants that can be applied to any toric
Calabi-Yau with involution. We then show that the full topological string
amplitudes can be reproduced within the topological vertex formalism. We obtain
the real topological vertex with trivial fixed leg. Finally, we verify that the
same results derive in the B-model from the extended holomorphic anomaly
equation, together with appropriate boundary conditions. The expansion at the
conifold exhibits a gap structure that belongs to a so far unidentified
universality class.
