  In this paper we consider germs of k-parameter generic families of analytic
2-dimensional vector fields unfolding a saddle-node of codimension k and we
give a complete modulus of analytic classification under orbital equivalence
and a complete modulus of analytic classification under conjugacy. The modulus
is an unfolding of the corresponding modulus for the vector field with the
saddle-node. The point of view is to compare the family with a "model family"
via an equivalence (conjugacy) over canonical sectors. This is done by studying
the asymptotic homology of the leaves and its consequences for solutions of the
cohomological equation.
