  We initiate the study of wall crossing phenomena in orientifolds of local
toric Calabi-Yau 3-folds from a topological string perspective. For this
purpose, we define a notion of real Donaldson-Thomas partition function at the
large volume, orbifold and non-commutative point in Kaehler moduli space. As a
byproduct, we refine the constant map contribution to the partition function of
the real topological string on a local toric background. We conjecture the
general relation between the real large volume and real
non-commutative/orbifold Donaldson-Thomas partition function of orientifolds of
local toric Calabi-Yau 3-folds without compact divisors. The conjectured
relation is confirmed at hand of the conifold and local A_n singularity, for
which we explicitly derive the real non-commutative/orbifold Donaldson-Thomas
partition function combinatorially.
