I have this happen a lot. In my email program (Outlook), I create a folder for each if these people, then make a rule to send all their emails to that folder. I check them about once a week to make sure there wasn't anything I needed to see, then delete everything in the folder without reading or even opening the rest.
To make a rule in Outlook, right click on the email, click Rules, click Create Rule, click the top check box, click the bottom check box, then click Select Folder. In the list, click Inbox, then click New. Name the new folder, click OK. Click OK again, and then click OK again. Click the checkbox in the Success box, then click OK. All the emails from that person will be moved to the folder you created. It will make reading other emails so much easier, since you will be able to find them easier.