Goodness of generic one-parameter families on the two-sphere

A family of vector fields on the two-sphere is called good when it is moderately structurally stable. A one-parameter family has a one-dimensional parameter space, and generic means belonging to the relevant generic class.

Good-family conjecture. Generic one-parameter families of vector fields in the two-sphere are good.

The conjecture is presented as part of a proposed division of finite-parameter families into good, bad and ugly classes. The source later says that a description of the possible degeneracies implies this one-parameter conjecture.