  The hyperbolicity statements for subvarieties and complements of
hypersurfaces in abelian varieties admit arithmetic analogues, due to Faltings
(and Vojta for the semi-abelian case). In Atti Accad. Naz. Lincei Rend. Lincei
Mat. Appl. 29 (2018) by the second author, an analogy between the analytic and
arithmetic theories was shown to hold also at proof level, namely in a proof of
Raynaud's theorem (Manin-Mumford Conjecture). The first aim of this paper is to
extend to the relative setting the above mentioned hyperbolicity results. We
shall be concerned with analytic sections of a relative (semi-)abelian scheme
over an affine algebraic curve.
  These sections form a group; while the group of rational sections (the
Mordell-Weil group) has been widely studied, little investigation has been
pursued so far on the group of the analytic sections. We take the opportunity
of developing some basic structure of this apparently new theory, defining a
notion of height or order functions for the analytic sections, by means of
Nevanlinna theory.
