Transfer from Terminal 3 to Terminal 1 in Beijing airport

Hi, I will be arriving from Vancouver to Beijing in T3 and leaving from T1 to Singapore in 9 hours. I am holding a Canadian passport and will not be leaving the airport. I do not need a visa right even though I am arriving in T3 and leaving from T1. Please advise because some say I need but most says I don't. I just want to confirm. Is there a passage I could connect from t3 to t1 without going through immigration? Thank you!!!!