The crime happened on the 2000 block of North Cleveland Street on November 15.
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The suspect, identified as 35-year-old Kyle Halls, was taken into custody on Thursday morning.
In a criminal complaint, the ATF said Halls broke a window before lighting a bottle of gasoline on fire and tossing it inside.
Halls' mother, Valerie Piner, said he called her from jail.
"He's not a hardened criminal. He has serious mental health issues and I've been going through this for years," she said.
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Piner said she's tried to get him help and that he's never done something like this.
She was relieved to know that everyone made it out of the home safely.
"My apologies to the family, or the persons, that had to endure this incredible devastation - of their home being destroyed - they had to endure," said Piner.
Halls is also charged in connection with several cases of car vandalism, and the ATF expects to soon file charges for the arson.
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