"On up and up" is an idiomatic expression that refers to something being honest, truthful or ethical. It implies that a person or a situation is genuine and trustworthy. The antonyms for "on up and up" are dishonest, unscrupulous, and deceitful. A person who is not "on up and up" can be described as being shady, fraudulent or corrupt. Such people engage in unethical behavior and might hide their true intentions. They are often not reliable and therefore cannot be trusted. In contrast, a person who is "on up and up" will always communicate honestly and be transparent in their dealings.