I will show that the space of pointed infinite volume hyperbolic 3-manifolds is connected but not path connected. This space is equipped with the geometric topology, in which two pointed manifolds are close if they are almost isometric on large neighborhoods of their basepoints. The proof of connectivity will be an application of the density theorem for Kleinian groups. I will then use a combination of results on representations of Kleinian groups and Chabauty spaces of subgroups to construct an infinite family of path components of this space.