SARAH EL DEEBGAZA CITY, Gaza Strip (AP) â¿¿ Mohammed Falah Azzam has been through this before. His mother's home was bombed in the 2008-09 Israeli military offensive in the Gaza Strip, which left hundreds dead and thousands of homes destroyed. In renewed fighting last week, an entire block of buildings housing his extended family was badly damaged in an airstrike that Israel said was aimed at a militant. While none of his relatives was hurt, the 61-year-old retired schoolteacher once again has to worry about providing shelter for his family. Some relatives are sleeping in an empty shop, squeezed in with other family members. Others are spending their nights in rooms covered in plastic wrap to shield them from the winter rain because all the windows were blown out. "This is going to cost thousands," Azzam said. "The longer I wait, the more damage will happen," he added, pointing to a heavily damaged building sitting atop tilting concrete columns. Azzam finds himself caught again in a pile of paperwork to seek assistance, trying to secure hard-to-get construction materials. This time, he hopes the process will be smoother, thanks to both Israel's pledges to ease its longstanding border blockade and the newfound political clout of Gaza's Hamas rulers in the region. Israel promised to ease the blockade as part of a cease-fire last week that ended eight days of intense fighting. But difficult negotiations lie ahead, and there is no firm timeline for lifting the restrictions. Israel launched its offensive Nov. 14 in response to months of rocket fire out of Gaza. It carried out some 1,500 airstrikes during the fighting, while Palestinian militants lobbed a similar number of rockets into Israel. The damage to buildings in Gaza appears less extensive than it was four years ago. The United Nations estimates 10,000 homes were destroyed or damaged, while Hamas has put the number at about 8,000, including 500 that were destroyed or heavily damaged. In comparison, U.N. relief agencies said as many as 40,000 homes were affected in the earlier round of fighting.