  In this work, we explore proof theoretical connections between sequent,
nested and labelled calculi. In particular, we show a general algorithm for
transforming a class of nested systems into sequent calculus systems, passing
through linear nested systems. Moreover, we show a semantical characterisation
of intuitionistic, multi-modal and non-normal modal logics for all these
systems, via a case-by-case translation between labelled nested to labelled
sequent systems.
