  Using the Batalin-Vilkovisky formalism, we study the Ward identities and the
equations of gauge dependence in potentially anomalous general gauge theories,
renormalizable or not. A crucial new term, absent in manifestly nonanomalous
theories, is responsible for interesting effects. We prove that gauge
invariance always implies gauge independence, which in turn ensures
perturbative unitarity. Precisely, we consider potentially anomalous theories
that are actually free of gauge anomalies thanks to the Adler-Bardeen theorem.
We show that when we make a canonical transformation on the tree-level action,
it is always possible to re-renormalize the divergences and re-fine-tune the
finite local counterterms, so that the renormalized $\Gamma $ functional of the
transformed theory is also free of gauge anomalies, and is related to the
renormalized $\Gamma $ functional of the starting theory by a canonical
transformation. An unexpected consequence of our results is that the beta
functions of the couplings may depend on the gauge-fixing parameters, although
the physical quantities remain gauge independent. We discuss nontrivial checks
of high-order calculations based on gauge independence and determine how
powerful they are.
