  Pseudocycles are geometric representatives for integral homology classes on
smooth manifolds that have proved useful in particular for defining
gauge-theoretic invariants. The Borel-Moore homology is often a more natural
object to work with in the case of non-compact manifolds than the usual
homology. We define weaker versions of the standard notions of pseudocycle and
pseudocycle equivalence and then describe a natural isomorphism between the set
of equivalence classes of these weaker pseudocycles and the Borel-Moore
homology. We also include a direct proof of a Poincar\'e Duality between the
singular cohomology of an oriented manifold and its Borel-Moore homology.
