We show how the techniques from the Okamoto-Sakai geometric theory of Painlevé equations can be used to solve the Painlevé equivalence, i.e., how to recognize an equation as a Painlevé equation and find an explicit change of variables transforming it into some canonical form. We illustrate the geometric approach by considering two examples recently obtained by M. van der Put and J. Top in their study of a certain ansatz of isomonodromic deformations of linear ODEs. We provide explicit coordinate transformations identifying these examples with standard form of some Painlevé equations and also explicitly identify their Hamiltonians.