  We prove the equivalence between Clifford-Severi inequalities for good
classes of varieties of maximal Albanese dimension and Slope Inequalities for
fibrations of such varieties over curves. This provides a big set of new Slope
Inequalities and characterizes the limit cases. It also gives a machinery to
automatically obtain other higher dimensional Slope and Clifford-Severi
inequalities from inequalities in low dimension. For this, we construct a
continuous version of Xiao's method for irregular fibrations.
