Note on the equivalence of different approximations in the relaxation theory

We briefly discuss relations between different variants of the second order generalized master equations (GME), in particular among different types of the Markov-Born approximation of time-convolution GME and Born approximation in time-convolutionless one. We prove that equivalence valid in the van Hove limit does not in general apply for other types of scaling. On the other hand, for other scalings one appropriate form of the interaction representation always exist that reproduces this equivalence known from the weak-coupling (van Hove) one.