  We explicitly compute the geometrical Berry phase for the noncommutative
gravitational quantum well for different SW maps. We find that they lead to
different partial contributions to the Berry phase. For the most general map we
obtain that $\Delta\gamma(S)\sim{\eta}^3$, in a segment S of the path in the
configuration space where $\sqrt{\eta}$ is the fundamental momentum scale for
the noncommutative gravitational quantum well. For the full closed path, we
find, through an explicit computation, that $\gamma(C)=0$. This result is
consistent with the fact that physical properties are independent of the SW map
and shows that these maps do not introduce degeneracies or level crossing in
the noncommutative extensions of the gravitational quantum well.
