Fibrations on Handlebodies

We show that the open genus 2 handlebody admits uncountably-many fibrations over the circle with fiber homeomorphic to the Cantor tree surface with non-conjugate monodromies in the mapping class group. The construction generalizes to produce uncountably many fibrations of other tame 3-manifolds with infinite type fibers, including the blooming Cantor tree and many other types of surfaces.