Following tests of Twitter-style Trending Topics on the web and mobile in August, Facebook on Thursday officially launches a redesigned “Trending” section on its web homepage’s sidebar in the US, UK, Canada, India and Australia. The richer design shows personalized lists of the most mentioned words and phrases of the moment with short explanations of why each is blowing up. A click-through leads to a Page of mentions by friends, Pages, and public posts by anyone who lets people “Follow” them. If Facebook users find the Trending section atop the right sidebar of their homepage useful, it could encourage public sharing, drive return visits, and most importantly — make Facebook better known as a news source for current events. The social network has been in a heated battle with Twitter for that distinction over the past few years.