Is it possible to use the green bar in the Timeline to erase keyframes?
Is there someway to do something like erasing keyframes by scrolling over them instead of removing them one by one?
No; not in the timeline.
This is done in the Dope Sheet.
Hit X to delete selected keyframes.
It is possible to delete the keyframes from the 3D view without having to have one of the animation views visible but it doesn't remove the problem of having to delete the keyframes one by one.
Move to the timeline marker to the frame that has the keyframe you want to delete.
With the cursor in the 3D view press Alt+I and choose 'Delete Keyframe'.
This will delete all keyframes on the current frame but still has to be done on every separate frame.
There is another way to erase keyframes (This method allows you to select precisely which property to delete key):
Right-click on it, and select Delete keyframes, or Delete Single Keyframe (the first will delete all 3 location property keys, and the second only the property you right-clicked on, i.e. X, Y, or Z).
The given answers are ok for a few objects with keyframes, but if you have a lot of objects. Then select all objects, go in the graph editor and hit A to select all keyframes. Then X to delete all selected. All keyframes are gone in more less steps.
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