On the structure of Takahashi Manifolds

We study the topological structure of the closed orientable 3-manifolds obtained by Dehn surgeries along certain links, first considered by Takahashi. The interest about such manifolds arises from the fact that they include well-known families of 3-manifolds, previously studied by several authors, as the Fibonacci manifolds, the Fractional Fibonacci manifolds, and the Sieradski manifolds, respectively. Our main results states that the Takahashi manifolds are 2-fold coverings of the 3-sphere branched along the closures of specified 3-string braids. We also describe many of the above-mentioned manifolds as n-folds cyclic branched coverings of the 3-sphere.