Twitter launched push notifications for @mentions. "Whenever an account that you follow mentions you, you'll immediately receive a notification in real-time. Notifications for @mentions will initially be available on SMS."
In addition to @mentions, push notifications for Messages also added to Twitter for iPhone. To turn on SMS notifications, go to twitter.com/devices and check the boxes under "Text message notifications". You can change your notifications settings at any time. For e.g., text "set mentions all" to turn on notifications for @mentions from everyone, rather than just those whom you follow, and "set mentions off" to turn off @mentions notifications.
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