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We prove a Reidemeister Theorem providing a set of combinatorial moves sufficient to relate the projections of isotopic links. We also show that any link admits a crossingless projection to any special spine and we refine our theorem to provide a set of combinatorial moves sufficient to relate crossingless diagrams. Finally, we discuss the connection to Turaev\u2019s shadow world, interpreting our result as a statement about shadow equivalence of a class of 4-manifolds.<\/jats:p>","DOI":"10.1007\/s00454-023-00539-4","type":"journal-article","created":{"date-parts":[[2023,8,31]],"date-time":"2023-08-31T21:01:31Z","timestamp":1693515691000},"page":"1190-1209","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Arc Diagrams on 3-Manifold Spines"],"prefix":"10.1007","volume":"71","author":[{"given":"Jack","family":"Brand","sequence":"first","affiliation":[]},{"given":"Benjamin A.","family":"Burton","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0598-3689","authenticated-orcid":false,"given":"Zsuzsanna","family":"Dancso","sequence":"additional","affiliation":[]},{"given":"Alexander","family":"He","sequence":"additional","affiliation":[]},{"given":"Adele","family":"Jackson","sequence":"additional","affiliation":[]},{"given":"Joan","family":"Licata","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,8,31]]},"reference":[{"key":"539_CR1","doi-asserted-by":"crossref","unstructured":"Alexander, J.W., Briggs, G.B.: On types of knotted curves. 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