On this page I'm attaching three lists of veering isosigs corresponding to complements of two-bridge links:
The first is a list of veering isosigs from the veering census which are also two-bridge links. There are only twenty.
Sakata shows that the Sakuma-Weeks triangulations of the two-bridge links associated to the continued fraction \([2,\dots,2]\) are veering. The second list contains the first 50 of these.
Triangulations in this family are always geometric. The first triangulation in the list is the two-tetrahedron triangulation of the figure-8 knot. The last triangulation in the list has 198 tetrahedra. They alternate between having one and two cusps.
Taking the Sakuma-Weeks triangulation of the two-bridge link associated to the continued fraction \([3,2,2,\dots,2,2,3]\) and performing two specific 3-2 moves gives a triangulation which is veering. I will write down a proof of this eventually. The third list contains the first 50.
Triangulations in this family are always geometric. The last one in the list has 200 tetrahedra. These always have two cusps, with one containing two ladders and the other containing \(2n+2\) ladders, where \(n\) is the number of 2's in the list. The volumes of these get arbitrarily large (because e.g. this paper).