The three men, all in their 30s, were being questioned by detectives, police said in a statement on Wednesday.
"Whilst we will not disclose further details at this stage, we stress that there remains no evidence that the events of Sunday night are in any way terrorist related", police said.
The blast in the central English city, which also injured five others,ripped through a building, destroying a convenience store on the ground floor and a two-storey apartment above.
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