Alitalia, the Italian airline, has started a new daily service from Kennedy International Airport in New York to Palermo, Sicily, via Milan's Malpensa Airport. Passengers change planes at Malpensa instead of having to transfer from Malpensa to Milan's Linate Airport, as they did previously.

To celebrate the service, the airline offers - through March 31 - a $100 discount off advance-purchase round-trip fares. Before discount, economy fares paid 14 days in advance are $871 on weekends and $807 midweek. The flight departs Kennedy at 7:30 p.m. and is scheduled to arrive in Palermo next day at 1:40 p.m.

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A Chinese garden, said to be the largest of its kind outside Asia, is scheduled to open in Montreal next June. The plan for the five-acre garden within the Montreal Botanical Garden includes an elaborate composition of waterways, rock gardens, hills, plants and pavilions with carvings.

The design derives from a style known as Meng Hu Yuan, or Dream Lake Garden, which originated during the Ming dynasty (A.D. 1368-1644). Chinese administrators stationed far from their homes, built gardens. The style is also known as the Yangtze style, because many of the officials who built the gardens were from the cities along the Yangtze River west of Shanghai.

The $4 million project was conceived in 1987 as a symbol of friendship between Montreal and Shanghai. The garden's wood carvings and peony trees and 300 of the 2,300 tons of stone came from China. About 50 people from Shanghai are working at the site under the supervision of Lei Wei-Zhong, of Shanghai, a garden designer of the Yangtze school. Interiors of the pavilions were completed last month.

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To give the artisans of the battered Kashmir Valley an outlet for their crafts now that the local tourist industry has collapsed because of separatist conflict, the state government of Jammu and Kashmir has built an outdoor crafts bazaar in the Indian capital.

Tucked into a piece of open ground between the state government emporiums on Baba Kharak Singh Marg, near Connaught Place in central Delhi, dozens of stalls will offer bargains from Kashmir throughout the winter. Called Kashmir Expo 90, the craft fair opened Nov. 5 and is expected to go on until the beginning of February.

More than 80,000 people in Jammu and Kashmir lived on traditional handicrafts - weaving, furniture and woodcarving, carpet making and papier-mach'e work being among the best known.

The permanent Jammu and Kashmir State Emporiums in Delhi will be well stocked this winter. One is near the outdoor Expo at 7A Baba Kharak Singh Marg and the other at 5 Prithviraj Road. Both are open Monday to Saturday 10 a.m. to 6 p.m.