  In this paper we give complete analytic invariants for germs of holomorphic
foliations in $(\mathbb{C}^2,0)$ that become regular after a single blow-up.
Some of them describe the holonomy pseudogroup of the germ and are called
transverse invariants. The other invariants lie in finite dimensional complex
vector space. Such singularities admit separatrices tangent to any direction at
the origin. When enough separatrices coincide with their tangent directions (a
condition that can always be attained if the mutiplicity of the germ at the
origin is at most four) we are able to describe and realize all the analytical
invariants geometrically and provide analytic normal forms. As a consequence we
prove that any two such germs sharing the same transverse invariants are
conjugated by a very particular type of birational transformations. We also
provide the first explicit examples of universal equisingular unfoldings of
foliations that cannot be produced by unfolding functions. With these at hand
we are able to explicitely parametrize families of analytically distinct
foliations that share the same transverse invariants.
