  This paper gives a proof that the universal cover of a closed 3-manifold
built from three $\pi_1$-injective handlebodies is homeomorphic to $\mathbb
R^3$. This construction is an extension to handlebodies of the conditions for
gluing of three solid tori to produce non-Haken Seifert fibered manifolds with
infinite fundamental group. This class of manifolds has been shown to contain
non-Haken non-Seifert fibered manifolds.
