I think there are two different issues at play here:
- What (if any) taxes do you have to pay at source?
- What (if any) taxes do you have to pay at the end of the year via a tax return?
From the example in your question, if you're living and working and employed in Sweden in January and February, you'll be having tax deducted at source by your Swedish employer on behalf of the Swedish government. The rate of tax of that will most likely be on the basis that you'll spend the whole year earning at that rate in Sweden.
Next, you move to Canada, cease working in Sweden, cease living in Sweden, and start working + living in Canada. At this point, you'll begin paying Canadian taxes at source, having the taxes deducted from your Canadian pay cheque.
Finally, at the end of the year, you will certainly need to complete a Canadian tax return, because you will be deemed to have been a Canadian Tax Resident for the year. On that, you'll list your Canadian income and your Swedish income from the year. You'll also list the Swedish taxes you've already paid - the Canadian-Swedish double tax treaty will allow you to claim those again your Canadian tax bill (within certain rules)
You may also need to complete a Swedish tax return too for the transition year. That will depend on the Swedish rules, and if they considered you to be tax resident there as well for the year, or not. (If you're not sure, either ask a suitable accountant, or ring up the Swedish tax office to check, or both! If you guess and guess wrong, you could be hit with fines/penalties/interest/etc if they later investigate and decide you have underpaid/failed to file/etc)
If you're subject to two tax jurisdictions, you will end up having to pay taxes in two countries, and overall at the higher rate. (eg country A has a 50% tax rate for you, country B has a 40% one, you pay taxes normally in country B at 40%, then complete the A return and give them the other 10%)
Oh, and one other thing - you may have been expecting certain favourable tax treatments on things in Sweden (eg pension contributions, tax free savings schemes etc). The Canadians may or may not accept those as being eligible for the same tax reliefs, it will depend on the Canadian-Swedish agreement. So, you may end up having to pay more tax than planned, if the Canadians don't recognise some Swedish tax breaks.