  We revisit Dimofte-Gaiotto-Gukov's construction of 3d gauge theories
associated to 3-manifolds with a torus boundary. After clarifying their
construction from a viewpoint of compactification of a 6d $\mathcal{N}=(2,0)$
theory of $A_1$-type on a 3-manifold, we propose a topological criterion for
$SU(2)/SO(3)$ flavor symmetry enhancement for the $u(1)$ symmetry in the theory
associated to a torus boundary, which is expected from the 6d viewpoint. Base
on the understanding of symmetry enhancement, we generalize the construction to
closed 3-manifolds by identifying the gauge theory counterpart of Dehn filling
operation. The generalized construction predicts infinitely many 3d dualities
from surgery calculus in knot theory. Moreover, by using the symmetry
enhancement criterion, we show that theories associated to all hyperboilc twist
knots have surprising $SU(3)$ symmetry enhancement which is unexpected from the
6d viewpoint.
