Yahoo Mail web by default offers a single message inbox view. So, for reading and replying to messages, you need to switch back and forth to the inbox to open different messages.
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There is an option through which you can enable tabbed messages for this inbox.
Here is how:
Login to your Yahoo Mail web version and click the Settings icon from the top right.
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From the menu, scroll to the Message tabs section and enable it.
On enabling, the Yahoo Mail inbox will reload and now you can open multiple messages as different tabs.
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You can then switch to different tabs to view and reply to messages.
By the way, Gmail offers a more powerful feature of multiple inboxes for better email management.
Happy emailing.