I believe you're looking for page 211 of Hyperbolic Structures on 3-Manifolds I: Deformation of Acylindrical Manifolds (Annals of Math., 1986), which includes the following paragraph:
A complete description of the three spaces $AH(M)$, $GH(M)$, and $QH(M)$ is
certainly not rigorously known, but here is a conjectural image, of which certain
features can be rigorously proved. Let us stick to the case that $M$ is a compact, acylindrical manifold. Then $H(M)$ is a hard-boiled egg. The egg complete with
shell is $AH(M)$; it appears to be homeomorphic to a closed unit ball. $GH(M)$ is
obtained by thoroughly cracking the egg shell on a convenient hard surface.
Apparently no material is physically separated from the egg, but many cracks are
developed - cracks are dense in the boundary - and at the same time, the
material of the egg just inside the shell is weakened, so that neighborhood
systems of points on the boundary become thinner. Finally, $QH(M)$ has uncountably many components, which are obtained by peeling off the shell and
scattering the pieces all over. Each component is homeomorphic to some
Teichmuller space - it is parametrized by Euclidean space of some even dimension. "Most" of the components have dimension zero, for they describe groups
whose limit set is all of $S_\infty^2$.
Here $H(M)$ is the set of complete hyperbolic manifolds $N$ with a homotopy equivalence $f:M\to N$, $AH(M)$ is $H(M)$ equipped with the 'algebraic topology', $GH(M)$ with the 'geometric topology', and $QH(M)$ with the 'quasi-isometric topology'.