We use a dedicated quotient operation called winding to give a new characteriz- ation of orientable cyclic orders; the characterization is twofold, in terms of partial orders and of separation properties. For this, we show the application to Petri nets: by winding causal nets, one obtains cyclic orders on synchronization graph that yield live and safe markings and describe the concurrent behavior of the system under these markings. Moreover, we characterize admissible action refinements on such nets by quotients of the corresponding (cyclic or acyclic) order structure.