NEW YORK (AP) — Retailers in the U.S. have used giveaways and bigger-than expected discounts to reward shoppers who ventured out on Black Friday. The day after Thanksgiving still reigns for now as the unofficial kickoff of the holiday shopping season even if it’s lost some luster. Analysts reported seeing the biggest crowds at stores that offered real savings. They say many shoppers are being cautious with their discretionary spending despite the easing of inflation. Stores are even more under the gun to get shoppers in to buy early and in bulk since there are five fewer days between Thanksgiving and Christmas this year. Online sales figures from Thanksgiving Day gave retailers a reason to remain hopeful for a lucrative end to the year.