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In this paper, we continue to study factorization of supersymmetric (SUSY)transformations in one-dimensional Quantum Mechanics into chains of elementaryDarboux transformations with nonsingular coefficients. We define the class ofpotentials that are invariant under the Darboux - Crum transformations andprove a number of lemmas and theorems substantiating the formulated formerlyconjectures on reducibility of differential operators for spectral equivalencetransformations. Analysis of the general case is performed with all thenecessary proofs.

Factorization of non-linear supersymmetry in one-dimensional Quantum Mechanics. II: proofs of theorems on reducibility