We show how equidimensional correpondences can be used to construct transforms on currents to provide explicit regulator maps from Higher Chow Groups of quasi projective varieties to Deligne Beilinson cohomology with integral coefficients. A fundamental ingredient in the construction is Suslin's moving lemma, showing that complexes of equidimensional correspondences are quasi-isomorphic to Bloch's original complex. This is joint work with Pedro dos Santos and Robert Hardt.