  We present some effective approaches in studying the relative monodromy group
of elliptic logarithms with respect to periods of elliptic schemes. We provide
explicit ways of constructing explicit loops which leave periods unchanged but
along which logarithms have non-trivial variations. We also get some
topological methods and effective results which allow to manage the
ramification locus of sections. The paper was inspired by a theorem of Corvaja
and Zannier which abstractly determine the relative monodromy group of
non-torsion sections.
