Oven shuts down the power in the whole appartment when it heats up
Had an electrician over who confirmed that the oven and all the wiring in the apartment was in perfect condition. He was puzzled himself, then told to me to hang on and dialed some phone number and after 20 minutes on the phone he found the solution. 

Turns out that the power company placed a limiter on my apartment's line because the new renter picked up the power service a bit later than the rules allowed. Basically if one renter stops his/her power service and there is no one who picks up the power service within few weeks, the power company (Epcor in Edmonton) places a limiter on the line. You still get the power at the apartment but if you exceed a certain power flow - the limiter shuts down the power in your unit. Here is more about this: 
https://www.epcor.com/learn/meters/Pages/power-meter-limiters.aspx

Thank you all for your suggestions. Lesson learned.