A white Mercedes van was reported to have been set alight in the Avondale area at 6.55am.
Later at 7.30am, a blue Vauxhall Meriva was also set on fire nearby.
Police also received a report of a blue Ford Ka which was set alight in The Isles area at 6.40am.
All the vehicles were extensively damaged.
Police are investigating a link between the attacks and have appealed for anyone with information to come forward.
Paul Madden, who has lived in the area for 25 years, had his car gutted and the garage of his home set on fire.
He says his family have been left very upset.
"Tears came to the eye you know, because we didn't need this sort of thing," he told UTV.
"My young son, who has Down's syndrome, is very upset. We need the car to take him out every day of the week.
"It's left us not very happy; you ask questions about why? Why did it come to us."
Adrian Watson, local UUP councillor, described the attacks as "unjustified vandalism and criminal damage".
He said two of the families targeted were elderly and have lived in the area for many years.
"They have been carried out on totally innocent people, people who were in their beds, totally unaware," he said.
"Thankfully a good Samaritan passing by raised the alarm and got these people out of their beds.
"Her actions potentially saved lives, because the flames at that stage had engulfed a garage at a house, at the other dwelling the flames were coming on to the roof of their home.
"If it hadn't been discovered, if five or ten minutes had elapsed, who knows what we would have been facing in Antrim this morning?"
Mr Watson added: "It could have been quite horrific, these people could have been killed in their beds."
Police are also investigating a separate report that a white Mini was set alight in a car park at the Top of the Town bar at 2.50am on Saturday.
Meanwhile in the early hours of Friday a nursery and a nearby car was set alight during a burglary in the Springfarm Road.
It is not known if anything was taken but the vehicle was destroyed.