Violence is up in the Big Apple’s transit system — with robberies and murders surging — even as overall crime underground is down, according to NYPD data.

A maniac repeat-offender pushed an elderly man to his death on Manhattan subway stairs Thursday, cops said — the fourth subway homicide this year, a 300% spike from the one murder at the same time last year.

Cops brought Rhamell Burke, described as an “emotionally disturbed person,” to Bellevue Hospital’s psych ward at 3:30 p.m. Thursday. He was released an hour later and at 9:30 p.m. allegedly shoved Ross Falzone, a 76-year-old retired teacher, down the stairs of a Chelsea subway station.

Rhamell Burke allegedly pushed a man to his death in the subway.…