In a large stainless steel saucepan, combine the apple cider and maple syrup, mixing thoroughly.
Take a clean square of cheesecloth and place the cinnamon sticks, cloves, allspice berries, and the orange and lemon peels in the center. Gather the edges of the cheesecloth and secure it with kitchen string to form a spice pouch. Add this pouch into the cider mixture.
Heat the saucepan over moderate heat. Allow the cider to warm until steaming, taking care not to let it boil, which should take around 5 to 10 minutes.
Once warmed, take the pan off the heat and remove the spice pouch, discarding it.
Serve the warm cider into large cups or mugs, and if desired, add a fresh cinnamon stick for added decoration and flavor. Enjoy!