  Recently, a large class of 3d $\mathcal{N} = 2$ gauge theories with mixed
Chern-Simons levels, corresponding to plumbing 3-manifolds, has been
identified. In this paper we generalize these theories by including in their
content chiral multiples, and analyze their properties. We find that the
content of such theories can be encoded in graphs, which generalize plumbing
graphs, and various operations in these theories can be represented in terms of
transformations of such graphs. The operations in question include gauging
global symmetries, integrating out gauge nodes, which for theories without
chiral multiplets corresponds to Kirby moves, and ST-transformations that
involve chiral multiplets. The dualities such as mirror triality and SQED-XYZ
duality can be also represented in terms of graphs, and enable us to find many
new dual theories by gauging global symmetries. In particular, we find that
gauged SQED-XYZ duality leads to other dualities, which take the same form as
operations of linking and unlinking discussed in the context of knots-quivers
correspondence. We also find that the superpotential can be encoded in an
interesting class of triangle graphs that satisfy certain consistency
conditions, we discuss decoupling and Higgsing of chiral multiplets, as well as
interpretation of various phenomena in terms of brane webs.
