Hospitalizations for asthma have been dramatically cut by a program that helps families reduce the conditions that trigger attacks, saving $1.46 in hospital care for every $1 spent on prevention, according to a Children's Hospital Boston study released Monday. The hospital's program, the Community Asthma Initiative, targeted 283 children with asthma in some of Boston's poorest neighborhoods. Health workers taught families how to correctly use medications and eliminate triggers of attack, such as contaminated bedding and feather dusters. After the first year, asthma-related emergency room visits for children in the program plummeted 68 percent compared with their emergency room trips in the year before enrolling, and there was an 85 percent drop in hospitalizations, according to the study published online in the journal Pediatrics.