  Understanding how tangential singularities evolve under smoothing processes
was one of the first problem concerning regularization of Filippov systems. In
this paper, we are interested in $C^n$-regularizations of Filippov systems
around visible regular-tangential singularities of even multiplicity. More
specifically, using Fenichel Theory and Blow-up Methods, we aim to understand
how the trajectories of the regularized system transits through the region of
regularization. We apply our results to investigate $C^n$-regularizations of
boundary limit cycles with even multiplicity contact with the switching
manifold.
