Desingularization of finite smooth vector fields on a plane

In this paper we consider desingularization of finite smooth vector fields. Let difference of germs of a finite smooth vector field and an analytic vector field be flat enough at a common singular point. Then these vector fields share similar behaviors under desingularization. In particular, the nice desingularizations of both vector fields are achieved in the same number of steps. Moreover, for any analytic vector field with a singular point of multiplicity $\mu_0$ the nice desingularization of the finite smooth vector field is achieved in $\mu_0+2$ steps. In addition in the article there is a description of topologically sufficient jets of finite smooth vector fields at non-monodromic singular points.