Berkovich spaces and tubular descent

We consider an algebraic variety XX together with the choice of a subvariety ZZ. We show that any coherent sheaf on XX can be constructed out of a coherent sheaf on the formal neighborhood of ZZ, a coherent sheaf on the complement of ZZ, and an isomorphism between certain representative images of these two sheaves in the category of coherent sheaves on a Berkovich analytic space WW which we define.