  Generically, the set of points along which two non-singular vector fields on
the three-sphere are positively (resp. negatively) collinear form a link. We
prove that the two vector fields are homotopic if and only if the linking
number of those links is zero. We use this criterion to give a new proof of a
result of Yano: every non-singular vector field on the three-sphere is
homotopic to a non-singular Morse-Smale vector field.
