Geodesic
Orientations of spines of homology balls
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 5, Tome 267 (2000), pp. 156-162

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Oriented special spines of 3-manifolds are studied. (Orientation is an additional structure on the spine, and each 3-manifold possesses a special spine with such a structure.) The moves $M^{\pm1}$ and $L^{\pm1}$ of special spines, which do not change the manifold, are well known. We prove that $M^{+1}$ and $L^{+1}$ preserve orientability of a spine, while $M^{-1}$ and $L^{-1}$ do not. For spines of homology balls, a class of moves is described which allow one to pass from a given orientation of a spine to any other orientation of the spine. 
@article{ZNSL_2000_267_a10,
     author = {A. Yu. Makovetskii},
     title = {Orientations of spines of homology balls},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {156--162},
     publisher = {mathdoc},
     volume = {267},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2000_267_a10/}
}
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A. Yu. Makovetskii. Orientations of spines of homology balls. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 5, Tome 267 (2000), pp. 156-162. http://geodesic.mathdoc.fr/item/ZNSL_2000_267_a10/