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What is definition of isotopy of pants decomposition in the following paper ?

when two pants decompositions is isotopic? Also why we say cut system what is definition of system ?

In Hatcher, Allen; Lochak, Pierre; Schneps, Leila, On the Teichmüller tower of mapping class groups, J. Reine Angew. Math. 521, 1-24 (2000). ZBL0953.20030..

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    $\begingroup$ A pants decomposition is a collection of 3g-3 curves. Two pants decompositions are isotopic if the curves are isotopic to each other. "system" here is just a word for collection. $\endgroup$
    – Gabriel Islambouli
    Commented May 26, 2022 at 16:58
  • $\begingroup$ @GabrielIslambouli . So here system is equal to collection ? $\endgroup$
    – Usa
    Commented May 26, 2022 at 17:22

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