  Finite stochastic Markov models play a major role for modelling biochemical
pathways. Such models are a coarse-grained description of the underlying
microscopic dynamics and can be considered mesoscopic. The level of
coarse-graining is to a certain extend arbitrary since it depends on the
resolution of accomodating measurements. Here, we present a way to simplify
such stochastic descriptions, which preserves both the meso-micro and the
meso-macro connection. The former is achieved by demanding locality, the latter
by considering cycles on the network of states. Using single- and multicycle
examples we demonstrate how our new method preserves fluctuations of
observables much better than na\"ive approaches.
