  The nature of the interaction between magnetism and topology in magnetic
topological semimetals remains mysterious, but may be expected to lead to a
variety of novel physics. We present $ab$ $initio$ band calculations,
electrical transport and angle-resolved photoemission spectroscopy (ARPES)
measurements on the magnetic semimetal EuAs$_3$, demonstrating a
magnetism-induced topological transition from a topological nodal-line
semimetal in the paramagnetic or the spin-polarized state to a topological
massive Dirac metal in the antiferromagnetic (AFM) ground state at low
temperature, featuring a pair of massive Dirac points, inverted bands and
topological surface states on the (010) surface. Shubnikov-de Haas (SdH)
oscillations in the AFM state identify nonzero Berry phase and a negative
longitudinal magnetoresistance ($n$-LMR) induced by the chiral anomaly,
confirming the topological nature predicted by band calculations. When magnetic
moments are fully polarized by an external magnetic field, an unsaturated and
extremely large magnetoresistance (XMR) of $\sim$ 2$\times10^5$ % at 1.8 K and
28.3 T is observed, likely arising from topological protection. Consistent with
band calculations for the spin-polarized state, four new bands in quantum
oscillations different from those in the AFM state are discerned, of which two
are topologically protected. Nodal-line structures at the $Y$ point in the
Brillouin zone (BZ) are proposed in both the spin-polarized and paramagnetic
states, and the latter is proven by ARPES. Moreover, a temperature-induced
Lifshitz transition accompanied by the emergence of a new band below 3 K is
revealed. These results indicate that magnetic EuAs$_3$ provides a rich
platform to explore exotic physics arising from the interaction of magnetism
with topology.
