Regarding the class d), it follows from Proposition 2.1 on page 31, that $$M(0,0;1/2,-1/2,\alpha/\beta)$$ is fiber-diffeomorphic to $$M(0,0;1/2,-1/2,\alpha'/\beta')$$ if and only if $$\alpha/\beta=\pm \alpha'/\beta'$$ if and only if $$M(-1,0;\beta/\alpha)$$ is fiber-diffeomorphic to $$M(-1,0;\beta'/\alpha')$$. But it is not clear to me, that for different $$q,q'\in\mathbb{Q}$$ with $$q,q'\geq 0$$ the manifolds $$M(-1,0;q)$$ and $$M(-1,0;q')$$ are not diffeomorphic and also not diffeomorphic to the manifolds under a),b),c),e), i.e. not diffeomorphic to the solid torus, the twisted $$I$$-bundle or the twisted $$S_1$$-bundle over the Klein bottle, or any lens space.