  We investigate anomalies on heterotic orbifolds and their blowups. We give a
simple example of an orbifold blowup which contains anomalous U(1) symmetries
that are canceled by axions which couple non-universally to the different gauge
groups, thus clarifying some confusion which recently arose in the literature
concerning anomaly universality. We argue that non-universal axionic couplings
are the general case, and that the couplings are only universal in the case of
orbifolds. We comment on the consequences of this non-universality for discrete
R symmetries. We furthermore investigate the origin of discrete (R and non-R)
symmetries on smooth Calabi-Yau manifolds.
