甲、乙双方可向各自当地法院提起诉讼 翻译成英文

　　Either party can bring its suit to the local court separately.

　　诉讼是指人民法院根据纠纷当事人的请求，运用审判权确认争议各方权利义务关系，解决经济纠纷的活动。
　　诉讼程序是在诉讼和司法过程中必须遵循的法定顺序、方式和步骤。
　　诉讼的功能不仅限于对过去发生之历史事实的发现，而更要通过诉讼的过程建立起过错与责任、犯罪与刑罚之间的联系,从而向公民传递一种应当如何行为的信息。

Both parties can appeal to the local court separately.
both parties指甲乙双方的当事人
appeal to v.呼吁；上诉；要求；对…有吸引力
local courts当地法院

甲、乙双方可向各自当地法院提起诉讼
Any party of the two can sue respectively in their place.

Each party can lodge a complaint to the local court

"起诉"也可是： sue 或者bring an action to the court against someone

Either party can bring its suit to the local court separately.