I'm trying to show that almost planar graphs are minor-closed. For that I need to show if $G-e$ is planar, then $G/e$ is almost planar (and vice versa).
My approach: I'm trying to show this using the fact that a planar graph has no $K_5$ or $K_{3,3}$ as a minor. So all I know is that if $G/e$ does have one of those as a minor, then the vertex to which $e$ has been contracted to, would be part of the minor (otherwise $G-e$ would also have them as a minor). I'm not sure how to go forward from here.