By Julia Boorstin, CNBC Correspondent
NEW YORK ( CNBC) -- Twitter is taking issue with the way Google favors Google+ over Twitter as it personalizes results for its new "Search plus your world" results. The two companies are shooting statements back and forth, establishing a battleground over instant search and potential anti-trust issues that is sure to become an even bigger issue in coming weeks. Google ( GOOG) is trying to make gains gains for its new social service, Google+, which aims to compete with both Facebook and Twitter. Twitter's general counsel, Alex Macgillivray, just tweeted an example of how Google's new search system impacts results when users are searching for @usernames. Check out the example Macgillivray shows in a screenshot, what happens when a user searches for @wwe. He's trying to make the point that though the "@" symbol makes it clear that a user is looking for a Twitter profile, Google chooses to suppress the Twitter result, instead promoting Google+ options.
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