Is ovarians cyst dangerous towards pregnancy. How to treat if it doenst disappeared by second trimester? If surgery required, would it affect the baby?

Not really. It depends on the size and type of cysts. If larger than 7 CM (size of a tennis ball) they can twist and cause severe pain & require surgery. If they don't have cancer characteristics (they look non-cancerous on ultrasound), leave them alone. You can have surgery safely in pregnancy if needed but best minimize risks to your baby and avoid it. Check with your doc for what's best for you.
Ovarian Cyst & Preg. Usually an ovarian cyst will not affect the pregnancy. Surgery for ovarian cysts in pregnancy are uncommon. We cannot be absolutely certain of cyst type until removed but ultrasound often helps us decide which ones to remove. Surgery in second trimester best and can be safe. Discuss with OB about your cysts to understand better. Good luck.