Yeah..it kinda has alot of meanings. According to a very reliable source:

occupy/busy oneself (with), be occupied (with), be engaged (in); engage (in); go in for, take up; indulge (in); devote oneself (to); concern oneself (with); attend (to)

also: learn, study

also: blaze/flare up, be set on fire, be on fire, catch fire; break, dawn

заря занимается - day is breaking