  We compute the local Gromov-Witten invariants of certain configurations of
rational curves in a Calabi-Yau threefold. These configurations are connected
subcurves of the `minimal trivalent configuration', which is a particular tree
of P^1's with specified formal neighborhood. We show that these local
invariants are equal to certain global or ordinary Gromov-Witten invariants of
a blowup of P^3 at points, and we compute these ordinary invariants using the
geometry of the Cremona transform. We also realize the configurations in
question as formal toric schemes and compute their formal Gromov--Witten
invariants using the mathematical and physical theories of the topological
vertex. In particular, we provide further evidence equating the vertex
amplitudes derived from physical and mathematical theories of the topological
vertex.
