  We study heterotic $E_8\times E_8$ models that are dual to compactifications
of F-theory and type IIA string on certain classes of elliptically fibered
Calabi-Yau manifolds. Different choices for the specific torus in the fibration
have heterotic duals that are most easily understood in terms of $E_8\times
E_8$ models with gauge backgrounds of type $H\times U(1)^{8-d}$, where $H$ is a
non-Abelian factor. The case with $d=8$ corresponds to the well known
$E_8\times E_8$ compactifications with non-Abelian instanton backgrounds
$(k_1,k_2)$ whose F-theory duals are built through compactifications on
fibrations of the torus $\IP_2^{(1,2,3)}[6]$ over $\IF_n$. The new cases with
$d < 8$ correspond to other choices for the elliptic fiber over the same base
and yield unbroken $U(1)$'s, some of which are anomalous and acquire a mass by
swallowing zero modes of the antisymmetric $B_{MN}$ field. We also study
transitions to models with no tensor multiplets in $D=6$ and find evidence of
$E_d$ instanton dynamics. We also consider the possibility of conifold
transitions among spaces with different realization of the elliptic fiber.
