One of the Eilenberg-Steenrod axioms which states that, if f:(X, A)->(Y, B) is homotopic to g:(X, A)->(Y, B), then their induced maps f_* :H_n(X, A)->H_n(Y, B) and g_* :H_n(X, A)->H_n(Y, B) are the same.

homotopic | homotopy | homotopy theory