Transit crime in the Big Apple spiked nearly 11% last month — a surge cops partially blamed on violent and sticky-fingered recidivists Monday. July saw 173 transit crimes overall, compared to 156 during the same month last year, according to newly released NYPD statistics. The increase was largely fueled by felony assaults and non-violent grand larcenies, police officials said. Felony assaults accounted for 27% (47) of all transit crime during July, while grand larcenies — or thefts of property valued at more than $1,000 — made up 51.4% (88), officials said. Roughly half those felony assaults were committed against three…