  In this work we explore the physics associated to Calabi-Yau (CY) n-folds
that can be described as a fibration in more than one way. Beginning with
F-theory vacua in various dimensions, we consider limits/dualities with
M-theory, type IIA, and heterotic string theories. Our results include many
M-/F-theory correspondences in which distinct F-theory vacua - associated to
different elliptic fibrations of the same CY n-fold - give rise to the same
M-theory limit in one dimension lower. Examples include 5-dimensional
correspondences between 6-dimensional theories with Abelian, non-Abelian and
superconformal structure, as well as examples of higher rank Mordell-Weil
geometries. In addition, in the context of heterotic/F-theory duality, we
investigate the role played by multiple K3- and elliptic fibrations in known
and novel string dualities in 8-, 6- and 4-dimensional theories. Here we
systematically summarize nested fibration structures and comment on the roles
they play in T-duality, mirror symmetry, and 4-dimensional compactifications of
F-theory with G-flux. This investigation of duality structures is made possible
by geometric tools developed in a companion paper [1].
