In this paper, we give an isotopy classification of 3-bridge spheres of 3-bridge arborescent links, which are not Montesinos links. To this end, we prove a certain refinement of a theorem of J. S. Birman and H. M. Hilden  on the relation between bridge presentations of links and Heegaard splittings of 3-manifolds. In the proof of this result, we also give an answer to a question by K. Morimoto  on the classification of genus-2 Heegaard splittings of certain graph manifolds.
"Classification of 3-bridge spheres of 3-bridge arborescent links." J. Math. Soc. Japan 65 (1) 97 - 136, January, 2013. https://doi.org/10.2969/jmsj/06510097