We reinterpret the classical theory of cocyclic operations in terms of permutations and homotopy equivalences of explicit chains. The essential tools we use are Homological Perturbation Theory and Eilenberg-Zilber Theorem. The main objective of this technique is the final identification of cohomology operations at cochain level.
Homology Homotopy Appl.
7(2):
95-108
(2005).