  Let M be a possibly non compact smooth manifold. We study genericity in the
C^k-topology (3<=k<=+infty) of nondegeneracy properties of semi-Riemannian
geodesic flows on M. Namely, we prove a new version of the Bumpy Metric Theorem
for a such M and also genericity of metrics that do not possess any degenerate
geodesics satisfying suitable endpoints conditions. This extends results in the
literature for geodesics with fixed endpoints to the case where endpoints lie
on a compact submanifold P of MxM that satisfies an admissibility condition.
Immediate consequences are generic non conjugacy between two points and non
focality between a point and a submanifold (or also between two submanifolds).
