  Felsner introduced a cycle reversal, namely the `flip' reversal, for
\alpha-orientations (i.e., each vertex admits a prescribed out-degree) of a
graph G embedded on the plane and further proved that the set of all the
\alpha-orientations of G carries a distributive lattice with respect to the
flip reversals. In this paper, we give an explicit formula for the minimum
number of flips needed to transform one \alpha-orientation into another for
graphs embedded on the plane or sphere, respectively.
