  Heterotic orbifolds provide promising constructions of MSSM-like models in
string theory. We investigate the connection of such orbifold models with
smooth Calabi-Yau compactifications by examining resolutions of the T^6/Z6-II
orbifold (which are far from unique) with Abelian gauge fluxes. These gauge
backgrounds are topologically characterized by weight vectors of twisted
states; one per fixed point or fixed line. The VEV's of these states generate
the blowup from the orbifold perspective, and they reappear as axions on the
blowup. We explain methods to solve the 24 resolution dependent Bianchi
identities and present an explicit solution. Despite that a solution may
contain the MSSM particle spectrum, the hypercharge turns out to be anomalous:
Since all heterotic MSSM orbifolds analyzed so far have fixed points where only
SM charged states appear, its gauge group can only be preserved provided that
those singularities are not blown up. Going beyond the comparison of purely
topological quantities (e.g. anomalous U(1) masses) may be hampered by the fact
that in the orbifold limit the supergravity approximation to lowest order in
alpha prime is breaking down.
