The concept of arcbody was introduced in [4] as a generalization of prime tangles used by Lickorish[3] and Bleiler[l]. The pair ( A, l ), where A is a compact 3-manifold with boundary ∂ A , and l is a 1-submanifold properly embedded in A , is an arcbody if: (i) the inclusion ∂ A – l ↪ A – l is monic, i.e. A – l has incompressible boundary; (ii) no component of ( A, l ) is homeomorphic to ( D 2 , 0) × I or ( D 2 , 0) × S 1 ; and (iii) every sphere of ∂ A intersects l .