Yes, it will stay open until the master process finishes or you ask it to close the tunnel sending a cancel control: 
$ssh->system({ssh_opts => ['-O', 'cancel', '-L127.0.0.1:12345:127.0.0.
+1:3306']});

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In reply to Re^4: How do you use Net::OpenSSH to query mysql database via ssh tunnel by salva
in thread How do you use Net::OpenSSH to query mysql database via ssh tunnel by nysus

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