By Sarah McBride SAN FRANCISCO (Reuters) – App-based ride company Uber will start delivering on its promise of expanding its business into logistics on Tuesday when it launches a trial courier service, Uber Rush, in Manhattan. Better, faster, cheaper, is how Ubers general manager in New York, Josh Mohrer, described the service in a tweet to Reuters. At first, Uber Rush will work only in Manhattan, but if it catches on, it will expand to other boroughs and perhaps eventually, other cities, Mohrer said in a phone interview. Messengers can only pick up and deliver items, not purchase them, Uber said in a blog post.