Seifert manifolds and $(1,1)$-knots

The aim of this paper is to investigate the relations between Seifert manifolds and $(1,1)$-knots. In particular, we prove that each orientable Seifert manifold with invariants
$$ \{Oo,0|-1;\underbrace{(p,q),\dots,(p,q)}_{n\ \text{times}},(l,l-1)\} $$
has the fundamental group cyclically presented by $G_n((x^q_1\cdots x^q_n)^lx^{-p}_n)$ and, moreover, it is the $n$-fold strongly-cyclic covering of the lens space $L(|nlq-p|,q)$ which is branched over the $(1,1)$-knot $K(q,q(nl-2),p-2q,p-q)$ if $p\ge2q$ and over the $(1,1)$-knot $K(p-q,2q-p,q(nl-2),p-q)$ if $p<2q$.