  In this paper we present an analytical treatment of gravitational lensing by
Kerr black holes in the limit of very large deflection angles, restricting to
observers in the equatorial plane. We accomplish our objective starting from
the Schwarzschild black hole and adding corrections up to second order in the
black hole spin. This is sufficient to provide a full description of all
caustics and the inversion of lens mapping for sources near them. On the basis
of these formulae we argue that relativistic images of Low Mass X-ray Binaries
around Sgr A* are very likely to be seen by future X-ray interferometry
missions.
