  We have recently shown that the global behavior of the partition function of
N=2 gauge theory in the general Omega-background is captured by special
geometry in the guise of the (extended) holomorphic anomaly equation. We here
analyze the fate of our results under the shift of the mass parameters of the
gauge theory. The preferred value of the shift, noted previously in other
contexts, restores the Z_2 symmetry of the instanton partition function under
inversion of the Omega-background, and removes the extension. We comment on
various connections.
