Anechoic cysts tend to be filled with fluid so that is a good sign. Cysts related to ovarian cancer tend to be complex (with solid parts) and grow larger than 5cm. Most cysts (even complex ones) turn out to be benign. It is the general recommendation to watch and wait cysts that are simple and under 5cm. But, since your cyst is already 4.1 cm., I can see why your doctor has mentioned surgery as a possibility. It is possible for your cyst to go away on its own in time. There isn't anything you can do to prevent it from growing. Just be sure to keep your follow-up appointment with your doctor. Even benign cysts that grow large can cause problems. Best wishes!