K3 transitions and canonical 3-folds

We introduce K3 transitions as a geometric approach to studying canonical 3-folds. These transitions link different deformation classes of canonical 3-folds via a combination of birational contractions and smoothings. As applications, we investigate some basic properties of the web of canonical 3-folds in small codimension and give an interesting example of a singularity in codimension 4 with obstructed smoothings, similar to the famous example of the affine cone over a degree 6 del Pezzo surface.