Small perturbative fields in a synchrotron influence both the spin and orbital motion of a stored beam. Their effect on the beam polarization consists of two contributions, a direct kick and an effect of the ring lattice due to orbit perturbation. Spin response function is an analytic technique to account for both contributions. We develop such a technique for the spin-transparent synchrotrons where the design spin motion is degenerate. Several perspective applications are illustrated or discussed. In particular, we consider the questions of the influence of lattice imperfections on the spin dynamics and spin manipulation during an experiment. The presented results are of a direct relevance to NICA (JINR), RHIC (BNL), EIC (BNL) and other existing and future colliders when they arranged with polarization control in the spin-transparent mode.