  We present Integral Field Spectroscopic (IFS) observations of the nearby
($z\sim0.03$) dual Active Galactic Nuclei (AGN) Mrk 739, whose projected
nuclear separation is $\sim$3.4~kpc, obtained with the Multi Unit Spectroscopic
Explorer (MUSE) at the Very Large Telescope (VLT). We find that the galaxy has
an extended AGN-ionized emission-line region extending up to $\sim 20$ kpc away
from the nuclei, while star-forming regions are more centrally concentrated
within 2 - 3 kpc. We model the kinematics of the ionized gas surrounding the
East nucleus using a circular disk profile, resulting in a peak velocity of
$237^{+26}_{-28}$ km s$^{-1}$ at a distance of $\sim 1.2$ kpc. The enclosed
dynamical mass within 1.2 kpc is $\log M(M_{\odot})=10.20\pm0.06$, $\sim$1,000
times larger than the estimated supermassive black hole (SMBH) mass of Mrk
739E. The morphology and dynamics of the system are consistent with an early
stage of the collision, where the foreground galaxy (Mrk 739W) is a young
star-forming galaxy in an ongoing first passage with its background companion
(Mrk 739E). Since the SMBH in Mrk 739W does not show evidence of being rapidly
accreting, we claim that the northern spiral arms of Mrk 739W are ionized by
the nuclear activity of Mrk 739E.
