AFTER a long struggle to overcome the liabilities of his first term, Gov. Hugh L. Carey (D), 59, has finally achieved favorite's status in his bitter battle with state Assembly minority leader Perry B. Duryea (R), 56. The poll appearing today in Newsday and the Gannett papers gives Carey a 50-to-41 percent lead. Duryea has been on the defensive on his personal finances; the death penalty issue has lost some of its punch, and only an abnormally low turnout in New York City could sink Carey.

New York also has as many close House races as any state. Republicans pose serious threats to Reps. Jerome A. Ambro (D), Edward W. Pattison (D), James M. Hanley (D) and Richard L. Ottinger (D) - in roughly that order of vulnerability. The GOP is also making major bids in the districts of retiring Reps. Otis G. Pike (D) and James J. Delaney (D); it is favored in the former and a slight underlog in the latter. On the other hand, Rep S. William Green (R), winner of a 1977 special election in Manhattan's "Silk Stocking" district, is a slight underlog against Carter Burden (D), and ex-Rep. Peter A. Peyser, a Republican turned Democrat, is favored over Yonkers Mayor Angelo R. Martinelli (R) for the seat vacated by Rep. Bruce Caputo (R), Duryea's running-mate for lieutenant governor. Another Republican vacancy, that of retiring Rep. William F. Walsh (R), has both sides optimistic. Any net shift is likely to be in the Republican direction.