  In this work we explore the connections between (linear) nested sequent
calculi and ordinary sequent calculi for normal and non-normal modal logics. By
proposing local versions to ordinary sequent rules we obtain linear nested
sequent calculi for a number of logics, including to our knowledge the first
nested sequent calculi for a large class of simply dependent multimodal logics,
and for many standard non-normal modal logics. The resulting systems are
modular and have separate left and right introduction rules for the modalities,
which makes them amenable to specification as bipole clauses. While this
granulation of the sequent rules introduces more choices for proof search, we
show how linear nested sequent calculi can be restricted to blocked
derivations, which directly correspond to ordinary sequent derivations.
