The union that represents former Aveos workers is hoping a judge will grant an injunction to force Air Canada to obey court judgments.
The move comes as the Quebec government abandoned a court case against the airline despite two victories in court.
David Chartrand, a vice-president of the Quebec Federation of Labour, said Air Canada must respect the most recent court decision.
"That is why the Supreme Court was asked to hear and try to overturn that decision, but what legally is standing right now is the decision from the Court of Appeals where five, not one, not two, five people decided unanimously that Air Canada had to comply," said Chartrand.
The legal battle began in 2012 when Air Canada shut down its aircraft maintenance divisions in Montreal and Winnipeg and outsourced it to other countries, despite a federal law requiring such work be done in Canada.
Quebec's government took the airline to court and won in Superior Court and the Court of Appeal, so this past January Air Canada filed a petition to be heard in the Supreme Court of Canada.
In February the provincial government said it would no longer defend the 1,700 Aveos workers in exchange for Air Canada pledging to buy up to 75 CSeries jets from Bombardier, and a promise those planes would be maintained in Montreal starting in 2019.
The QFL said even though Quebec has abandoned the case, the Supreme Court has not yet agreed to hear the case, meaning the current judgment stands.
"The maintenance should be done if it's fleet here in Montreal urban community in Winnipeg and Mississauga and what we intend to do with the application we file today is to make sure that happens," said Chartrand.
Federal Transport Minister Marc Garneau has said the end of the lawsuits against Air Canada would provide the federal government with an opportunity to change the Air Canada Public Participation Act.
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