To study the topology of the deformation space of Kleinian groups, we need to understand the limiting object of a convergence sequence of Kleinian groups. We would focus on two types of convergence, the algebraic convergence and the geometric convergence. We would see, the two types of convergence of the same sequence might results in manifolds with different topological structures, and even when the two limits coincide as groups, the limiting group could give rise to manifolds with different homeomorphism types.