つうかん is the standard on'yomi. 通 (ツウ) means to pass through, and 関 (カン) means barrier or customs. つうこう, つうり, つうかく are incorrect readings of 関. This term refers to customs clearance, the process of getting goods cleared by customs authorities when importing or exporting, involving inspection and payment of duties.

つうかんは標準的な音読みです。通は「通る」、関は「関所」の意味。輸出入する貨物を税関の検査を経て通過させる手続きです。つうこう、つうり、つうかくは関の誤読です。