  Batyrev (et. al.) constructed a family of Calabi-Yau varieties using small
toric degenerations of the full flag variety G/B. They conjecture this family
to be mirror to generic anti-canonical hypersurfaces in G/B. Recently Alexeev
and Brion, as a part of their work on toric degenerations of spherical
varieties, have constructed many degenerations of G/B. For any such
degeneration we construct a family of varieties, which we prove coincides with
Batyrev's in the small case. We prove that any two such families are
birational, thus proving that mirror families are independent of the choice of
degeneration. The birational maps involved are closely related to Berenstein
and Zelevinsky's geometric lifting of tropical maps to maps between totally
positive varieties.
