  In $D=2+1$ dimensions there are two dual descriptions of parity singlets of
helicity $\pm 1$, namely the self-dual model of first-order (in derivatives)
and the Maxwell-Chern-Simons theory of second-order. Correspondingly, for
helicity $\pm 2$ there are four models $S_{SD\pm}^{(r)}$ describing parity
singlets of helicities $\pm 2$. They are of first-, second-,third- and
fourth-order ($r=1,2,3,4$) respectively. Here we show that the generalized
soldering of the opposite helicity models $S_{SD+}^{(4)}$ and $S_{SD-}^{(4)}$
leads to the linearized form of the new massive gravity suggested by
Bergshoeff, Hohm and Townsend (BHT) similarly to the soldering of
$S_{SD+}^{(3)}$ and $S_{SD-}^{(3)}$. We argue why in both cases we have the
same result. We also find out a triple master action which interpolates between
the three dual models: linearized BHT theory, $S_{SD+}^{(3)} + S_{SD-}^{(3)}$
and $S_{SD+}^{(4)} + S_{SD-}^{(4)}$. By comparing gauge invariant correlation
functions we deduce dual maps between those models. In particular, we learn how
to decompose the field of the linearized BHT theory in helicity eigenstates of
the dual models up to gauge transformations.
