  We consider topology changing transitions for M-theory compactifications on
Calabi-Yau fourfolds with background G-flux. The local geometry of the
transition is generically a genus g curve of conifold singularities, which
engineers a 3d gauge theory with four supercharges, near the intersection of
Coulomb and Higgs branches. We identify a set of canonical, minimal flux quanta
which solve the local quantization condition on G for a given geometry,
including new solutions in which the flux is neither of horizontal nor vertical
type. A local analysis of the flux superpotential shows that the potential has
flat directions for a subset of these fluxes and the topologically different
phases can be dynamically connected. For special geometries and background
configurations, the local transitions extend to extremal transitions between
global fourfold compactifications with flux. By a circle decompactification the
M-theory analysis identifies consistent flux configurations in four-dimensional
F-theory compactifications and flat directions in the deformation space of
branes with bundles.
