Flows without wandering points on compact connected surfaces

Given a compact $2$-dimensional manifold $M$ we classify all continuous flows $\varphi$ without wandering points on $M$. This classification is performed by finding finitely many pairwise disjoint open $\varphi-$invariant subsets $\{U_1, U_2, \ldots, U_n\}$ of $M$ such that $\bigcup_{i=1}^n{\overline{U_i}} = M$ and each $U_i$ is either a suspension of an interval exchange transformation, or a maximal open cylinder made up of closed trajectories of $\varphi$.