We show that in the mapping class group of a surface any relation between Dehn twists of the form ( a multitwist) is the lantern relation, and any relation of the form (where commutes with ) is the 2–chain relation.
"A lantern lemma." Algebr. Geom. Topol. 2 (2) 1179 - 1195, 2002. https://doi.org/10.2140/agt.2002.2.1179