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Police were first called to reports of a car on fire in Edgecliff about 3.20am on Tuesday, March 18.
A Mitsubishi SUV was found in flames.
Firefighters put the fire out, but the car had already been destroyed.
Police established a crime scene, but ten minutes later another fire was found.
Police found a burnt chair at the intersection of Glenmore Road and Cascade Street in Paddington.
Detectives now believe a third fire on Jersey Road in Paddington on September 19 last year is linked.
This morning, police released CCTV footage of a man who is believed to have been in the area at the time of the car fire.
He was described as being about 180cm tall with a medium build and long black hair.
Following the release of the footage, a 20-year-old man was arrested at Waverly Police Station.
Police say their investigation is ongoing.