Google and Barnes & Noble are working together to tackle their rival Amazon, by offering fast and cheap delivery of books. Starting on Thursday, book buyers in Manhattan, West Los Angeles and the San Francisco Bay Area will be able to get same-day deliveries from local Barnes & Noble stores through Google Shopping Express, Google’s online shopping and delivery service.

Google Shopping allows online shoppers to order products from stores like Costco, Walgreens, Staples and Target, and have them delivered to their doors within hours.

For Barnes & Noble, the partnership marks the company's first attempt to link the digital and physical book devivery. The company has closed 63 stores in the last five years, including some in bustling areas of Manhattan and Washington. Its Nook business fell 22 percent in the fourth quarter compared with the period a year earlier.

Amazon has already taken the lead in same-day delivery, and on Wednesday the company announced that it had expanded its same-day delivery service to 10 cities. Amazon’s same-day service costs $5.99 for members of its Prime program, and $9.98 for others. Walmart and eBay have also introduced same-day deliveries. Delivery is free for subscribers to Google Shopping Express, and costs $4.99 per delivery, per store for others. Membership is free for the first six months.