  The geometric quantization of a symplectic manifold endowed with a prequantum
bundle and a metaplectic structure is defined by means of an integrable complex
structure. We prove that its semi-classical limit does not depend on the choice
of the complex structure. We show this in two ways. First, by introducing
unitary identifications between the quantum spaces associated to the various
complex polarizations and second, by defining an asymptotically flat connection
in the bundle of quantum spaces over the space of complex structures.
Furthermore Berezin-Toeplitz operators are intertwined by these identifications
and have principal and subprincipal symbols defined independently of the
complex structure. The relation with Schrodinger equation and the group of
prequantum bundle automorphisms is considered as well.
