  An unknotting tunnel in a 3-manifold with boundary is a properly embedded
arc, the complement of an open neighborhood of which is a handlebody. A
geodesic with endpoints on the cusp boundary of a hyperbolic 3-manifold and
perpendicular to the cusp boundary is called a vertical geodesic. Given a
vertical geodesic in a hyperbolic 3-manifold M, we find sufficient conditions
for it to be an unknotting tunnel. In particular, if the vertical geodesic
corresponds to a 4-bracelet, 5-bracelet or 6-bracelet in the universal cover
and has short enough length, it must be an unknotting tunnel. Furthermore, we
consider a vertical geodesic that satisfies the elder sibling property, which
means that in the universal cover, every horoball except the one centered at
infinity is connected to a larger horoball by a lift of the vertical geodesic.
Such a vertical geodesic with length less than ln(2) is then shown to be an
unknotting tunnel.
