It is also known as the y-homeomorphism. This name was coined by Lickorish and the name crosscap slide was introduced by Korkmaz.
M. Korkmaz. Mapping Class Groups of Non-orientable Surfaces, Geometriae Dedicata 89 (2002), 109-133.
W.B.R. Lickorish. Homeomorphisms of non-orientable two-manifolds, Math. Proc. Camb. Phil. Soc. 59 (1963), 307-317.
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