<正>Weaddressthequestionthatifπ1-surjectivemapsbetweenclosedaspherical3-manifoldshavethesamerankonπ1theymustbeofnon-zerodegree.ThepositiveanswerisprovedforSeifertmanifolds,whichisusedinconstructingthefirstknownexampleofminimalHakenmanifold.Anothermotivationistostudyepimorphismsof3-manifoldgroupsviamapsofnon-zerodegreebetween3-manifolds.Manyexamplesaregiven.