  To examine the electronic phase diagram of superconducting CuO double chains,
we report the effect of external pressure on the magneto-transport properties
in superconducting and non-superconducting polycrystalline samples of
Pr$_{2}$Ba$_{4}$Cu$_{7}$O$_{15-\delta }$ at low temperatures (1.8-40 K) under
various magnetic fields (up to 14 T). In the as-sintered non-superconducting
sample, the magneto-resistance (MR) follows a power law of $H^{3/2}$ at low
temperatures, which is in no agreement with the $H^{2}$ dependence of MR in the
PrBa$_{2}$Cu$_{4}$O$_{8}$ system. The negative pressure dependence of the
superconducting phase is qualitatively consistent with a theoretical prediction
on the basis of the Tomonaga-Luttinger Liquid theory. The 48-h-reduced
superconducting sample at ambient pressure exhibits no clear increase in MR for
$T > T_{c,on}=26.5$ K. In contrast, with the application of pressure to the
superconducting sample, the MR effects reappear and are also well fitted by
$H^{3/2}$. The model of slightly warped Fermi surfaces explains not only the MR
effect of the non-superconducting sample, but is also related to the reasons
for the pressure-induced MR phenomena of the superconducting sample.
