The trio allegedly started the fire at a shop on Hinckley Road in Leicester using petrol on February 25th.
The three men, including the owner of the shop, appeared at Leicester magistrates court today, to face five charges of manslaughter and one of arson with intent to endanger life.
An explosion which killed five in Leicester was caused by petrol, a court has heard.
Another two men, both from East Anglia, are now in police custody and under questioning.
Mr Kurd, of Hillary Place, Leicestershire, Mr Hassan, of no fixed address and Mr Ali, of Drake Close, Oldham, will appear at Leicester Crown Court on 3 April via video link.
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Police confirmed on Friday that 18-year- old Leah Reek had been killed in the blast, following detailed forensic tests, along with her boyfriend Shane Ragoobeer (18) and his 17-year- old brother, Sean, who lived in the flat.
Three members of the same family died when the shop and flat were destroyed last Sunday.
Five people were taken to hospital after the explosion, including one with critical injuries.
The fifth body is still to be formally identified but is believed to be Ms Ragoobar. "A man in his 40s, from East Anglia, has been arrested on suspicion of manslaughter", local police said in a statement.