When I listen CNN daily news, the anchors must pronounce "City" as "Cidy"...t sound seems to be changed to "d" sound, but BBC anchors wouldn't change this sound......I was wondering if all the words have letter "t", then the Americans will change it to be "d" sound ?...please advise.
Read about flapping in American English. What you see is a flapping of intervocalic /t/. It is a feature of american english. You usually hear when t is not stressed.
for instance, Atom is pronounced as Adam, since the stress is on the first syllable.