The sale of MTS to Bell is not finalized and won't be until late 2016 early 2017 and that is only if the sale is approved by the Canadian Radio-television and Communications Commission.
Right now this does not change your products or services with MTS and there is no change to your billing or payment arrangements.
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In terms of services you have with MTS today things will stay as-is.
Over the next year MTS will continue to run as an independent company from Bell in case the purchase is not completed for any reason, such as it does to receive government/CRTC approval.
The next step most people will hear is either a second offer is made by another group to purchase MTS (unlikely) or that the CRTC has reached a decision and what that decision is.
Once the sale has final approval communication from Bell to MTS customers at that time would normally start. As Tennille mentions that is likely late in 2016 to early 2017 at the soonest.
Just a guess but the first round of notices to customers will be wireless customers moving to Telus as part of this deal. My speculation is these will be wireless-only customers in the Winnipeg market where Telus has the best coverage.
One final thing to note is much like MTS and Rogers have a wireless network sharing agreement currently, there is a similar agreement in place for Bell and Telus customers. This would mean after the deal wireless coverage would be the same regardless of which company is billing you.