  Let R be a Dedekind scheme, $\nu$ its generic point, X and V del Pezzo
surfaces of degree 1 over R that are Gorenstein Mori fiber spaces (as 3-folds
germs over the ground field). We study birational maps $\phi:X\dasharrow V$
over R which are isomorphisms over the generic point of R. We put down normal
forms of such transformations (in suitable coordinates) and give some
properties of X and V. In particular, we prove the uniqueness of a smooth
model.
