(eng): We present a simple characterizations of equivalent compositional model structures based on (A) invariant properties and (B) local transformations. It has been shown that one can transform any compositional model into Bayesian network representing the same joint probability distribution and vice versa. Moreover, every assertion of independence induced by a Bayesian network structure is also induced by the structure of the respective compositional model that is created from the Bayesian network and vice versa. That is why wa can simply compare characterization of equivalent compositional model structures together with the known characteristics of equivalent Bayesian network structures. We show which (A) invariant properties and (B)local transformations correspond each other. In opposite case we show what is its (invariant property, transformation) meaning in the other model structure.