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MR591141 (82i:57013) 57N12 (57M40)
Homma, Tatsuo; Ochiai, Mitsuyuki; Takahashi, Moto-o An algorithm for recognizing $S\sp{3}$ in $3$-manifolds with Heegaard splittings of genus two. Osaka J. Math. 17 (1980), no. 3, 625–648.
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