We parametrize the gauge-fixing freedom in choosing the Lagrangian of
a topological gauge theory. We compute the gauge-fixing dependence of
correlators of equivariant operators when the compactified moduli spac
e has a non-empty boundary and verify that only a subset of these has
a gauge independent meaning. We analyze in detail a simple example of
such anomalous topological theories, 4D topological Yang-Mills on the
four-sphere and instanton number k = 1.