  We try to give a geometric construction for 3d $\mathcal{N}=2$ gauge theories
using three-manifolds and Dehn surgeries. We follow the story that wrapping
M5-branes on plumbing three-manifolds leads to 3d theories with mixed
Chern-Simons levels. This construction can be decorated by adding non-compact
Lagrangian submanifolds in the cotangent bundles of three-manifolds. The
M5-branes wrapping on these submanifolds through M-theory/IIB string duality
lead to flavor D5-branes that engineer chiral multiplets. In this note, we only
consider unknotted matter circles, which are intersections between these
non-compact M5-branes and plumbing manifolds. Then various dualities of 3d
theories can be interpreted as Kirby moves and equivalent surgeries. We also
find the dictionary between geometric structures of three-manifolds and
physical aspects of gauge theories.
