  The classical formal equivalence upon a redefinition of the gauge connection
between Chern-Simons theory and topological massive Yang-Mills theory in
three-dimensional Euclidean space-time is analyzed at the quantum level within
the BRST formulation of the Equivalence Theorem. The parameter controlling the
change in the gauge connection is the inverse $\lambda$ of the topological
mass. The BRST differential associated with the gauge connection redefinition
is derived and the corresponding Slavnov-Taylor (ST) identities are proven to
be anomaly-free. The Green functions of local operators constructed only from
the ($\lambda$-dependent) transformed gauge connection, as well as those of
BRST invariant operators, are shown to be independent of the parameter
$\lambda$, as a consequence of the validity of the ST identities. The relevance
of the antighost-ghost fields, needed to take into account at the quantum level
the Jacobian of the change in the gauge connection, is analyzed. Their role in
the identification of the physical states of the model within conventional
perturbative gauge theory is discussed.
