  We consider the convergence of pointed multiply connected domains in the
Caratheodory topology. Behaviour in the limit is largely determined by the
properties of the simple closed hyperbolic geodesics which separate components
of the complement. Of particular importance are those whose hyperbolic length
is as short as possible which we call meridians of the domain. We prove a
continuity result on convergence of such geodesics for sequences of pointed
hyperbolic domains which converge in the Caratheodory topology to another
pointed hyperbolic domain. Using this we describe an equivalent condition to
Caratheodory convergence which is formulated in terms of Riemann mappings to
standard slit domains.
