2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58703We explain the essence of perturbation problems. The key to understanding is the structure of chain homotopy equivalence -- the standard one must be replaced by a finer notion which we call a strong chain homotopy equivalence. We prove an Ideal Perturbation Lemma and show how both new and classical results follow from this ideal statement.Introduction substantially revised and some typos correctedAlgebraic Topologytext