  We will prove the equivariant version of Smale's transversality theorem:
suppose that the compact Lie-group G acts on the compact differentiable
manifold M on which an invariant Morse-function f and an invariant vector field
X are given so that X is gradient-like with respect to f (i.e. X(f)<0 away from
critical orbits and X is the gradient of f (w.r.t. a fixed invariant Riemannian
metric) on some invariant open subsets about critical orbits of f.) Given a
bound $\epsilon>0$ we will prove the existence of an invariant vector field Y
of class C^1 for which vector field X+Y is also gradient-like such that:
  (a) |Y|_1<\epsilon (here |.|_1 is the C^1 norm).
  (b)The intersection of the stable and unstable sets of vector field X+Y taken
at a pair of critical orbits of f is transverse when restricted to an orbit
type of the action.
