  We give a finite presentation for the braid twist group of a decorated
surface. If the decorated surface arises from a triangulated marked surface
without punctures, we obtain a finite presentation for the spherical twist
group of the associated 3-Calabi-Yau triangulated category. The
motivation/application is that the result will be used to show that the
(principal component of) space of stability conditions on the 3-Calabi-Yau
category is simply connected in the sequel.
