We say that two toric models $({\mathcal{X}}_{i},D_{i},e_{i})$, $i=1,2$, are equivalent, if there exists a toric model $({\mathcal{X}}^{\prime},D^{\prime},e^{\prime})$ of $(X_{\Sigma},D_{\Psi})$ and morphisms of toric models $\alpha_{i}\colon{\mathcal{X}}^{\prime}\to{\mathcal{X}}_{i}$, $i=1,2$, such that $e^{\prime}\alpha_{i}^{\ast}D_{i}=e_{i}D^{\prime}$. This is an equivalence relation.