In the "Add a Gadget" panel on the right, search for "Dependency Map".
Add the gadget.
To configure the widget, enter the parent epic, set the Widget Height (e.g. 600) and click Save. You can also choose the type of link to use, e.g. Blocks, Clones, Duplicates, Relates.
The gadget should then render all stories in the epic with arrows representing dependencies.
Notes:
When filtering by issue status, the root nodes will remain visible regardless of the filter settings.