1. in conformity with sth ：following the rules of sth；conforming to sth
eg： regulations that are in conformity with European law
2. in accordance with sth (formal) ：according to a rule or the way that sb says that sth should be done
eg：in accordance with legal requirements
◆ We acted in accordance with my parents' wishes.
3. in compliance (with sth) (written) ：the practice of obeying rules or requests made by people in authority
eg：procedures that must be followed to ensure full compliance with the law
◆ Safety measures were carried out in compliance with paragraph 6 of the building regulations.
以上解释来源于牛津高阶词典,英文版.