  We use F-theory to study gauge algebra preserving transitions of 6d
supergravity theories that are connected by superconformal points. While the
vector multiplets remain unchanged, the hyper- and tensor multiplet sectors are
modified. In 6d F-theory models, these transitions are realized by tuning the
intersection points of two curves, one of them carrying a non-Abelian gauge
algebra, to a (4,6,12) singularity, followed by a resolution in the base. The
six-dimensional supergravity anomaly constraints are strong enough to
completely fix the possible non-Abelian representations and to restrict the
Abelian charges in the hypermultiplet sector affected by the transition, as we
demonstrate for all Lie algebras and their representations. Furthermore, we
present several examples of such transitions in torically resolved fibrations.
In these smooth models, superconformal points lead to non-flat fibers which
correspond to non-toric K\"ahler deformations of the torus-fibered Calabi-Yau
3-fold geometry.
