It is shown that the Topological Massive and "Self-dual" theories, which are known to provide locally equivalent descriptions of spin 1 theories in 2+1 dimensions, have different global properties when formulated over topologically non-trivial regions of space-time. The partition function of these theories, when constructed on an arbitrary Riemannian manifold, differ by a topological factor, which is equal to the partition function of the pure Chern-Simons theory. This factor is related to the

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... pace of solutions of the field equations of the Topological Massive Theory for which the connection is asymptotically flat but not gauge equivalent to zero. A new covariant, first order, gauge action,which generalize the "Self-dual" action, is then proposed. It is obtained by sewing local self-dual theories. Its global equivalence to the Topological Massive gauge theory is shown.