Homological Perturbation Theory summarizes several techniques in or- 

der to transfer structures between ob jects up to homotopy. In this setting, 

some fundamental concepts are the notions of chains contraction (special 

chain homotopy equivalence) and that of chain homotopy operators. In- 

stead of perturbing the differential graded modules involved, we obtain 

here some results about perturbation of chain homotopy operators. In 

particular, using a field as ring of coefficients, and as input a chain homo- 

topy operator φ : (C, d)  → (C, d)∗+1 over a differential graded module 

(C, d), which gives rise to a chain contraction from (C, d) to its homology, 

H (C, d), we can identify local perturbations of the homotopy operator (ε 

: (C, d) → (C, d)∗+1 ) that preserve the homology (that is, the homology 

H (C, φ) = H (C, φ + ε)). Some example are shown in the context of the 

homology of groups.