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We consider two filtrations\u2014one in <jats:italic>scale<\/jats:italic> obtained by fixing <jats:italic>k<\/jats:italic> and increasing\u00a0<jats:italic>r<\/jats:italic>, and the other in <jats:italic>depth<\/jats:italic> obtained by fixing <jats:italic>r<\/jats:italic> and decreasing <jats:italic>k<\/jats:italic>\u2014and we compute the persistence diagrams of both. While standard methods suffice for the filtration in scale, we need novel geometric and topological concepts for the filtration in depth. In particular, we introduce a rhomboid tiling in\u00a0<jats:inline-formula><jats:alternatives><jats:tex-math>$${{{\\mathbb {R}}}}^{d+1}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msup>\n                    <mml:mrow>\n                      <mml:mi>R<\/mml:mi>\n                    <\/mml:mrow>\n                    <mml:mrow>\n                      <mml:mi>d<\/mml:mi>\n                      <mml:mo>+<\/mml:mo>\n                      <mml:mn>1<\/mml:mn>\n                    <\/mml:mrow>\n                  <\/mml:msup>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> whose horizontal integer slices are the order-<jats:italic>k<\/jats:italic> Delaunay mosaics of\u00a0<jats:italic>X<\/jats:italic>, and construct a zigzag module of Delaunay mosaics that is isomorphic to the persistence module of the multi-covers.<\/jats:p>","DOI":"10.1007\/s00454-021-00281-9","type":"journal-article","created":{"date-parts":[[2021,3,31]],"date-time":"2021-03-31T15:03:00Z","timestamp":1617202980000},"page":"1296-1313","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["The Multi-Cover Persistence of Euclidean Balls"],"prefix":"10.1007","volume":"65","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9823-6833","authenticated-orcid":false,"given":"Herbert","family":"Edelsbrunner","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8882-5116","authenticated-orcid":false,"given":"Georg","family":"Osang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,3,31]]},"reference":[{"issue":"3","key":"281_CR1","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1007\/BF02187788","volume":"5","author":"F Aurenhammer","year":"1990","unstructured":"Aurenhammer, F.: A new duality result concerning Voronoi diagrams. 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