Flips from 4-folds with isolated complete intersection singularities

We investigate a flipping contraction g: X → Y from a 4-fold X with at worst isolated complete intersection singularities. If Y has an anti-bicanonical divisor (= bi-elephant) with only rational singularities, then g carries an inductive structure involving a chain of blow-ups (which we call La Torre Pendente), and in particular, the flip exists. This naturally contains Reid's "Pagoda" as an anticanonical divisor (= elephant) and its proper transforms.